No spoilers, but a reasonably detailed analysis of the series because I used to love it, even if now I have little interest in playing it at all.
First, the direct question; Do you need Mass Effect 1?
No. No you do not. In fact, to be entirely honest, if you wouldn't like ME1 on its own merits, it probably doesn't add a lot to ME2. That isn't saying that you had to think ME1 was perfect to get more out of ME2, it definitely had its problems, but if you couldn't overlook them for the lore and worldbuilding, the little nods back [And yes, that is all that ME2 does in regards to ME1, a couple of nods back] really aren't likely to engage you.
With ME2, Bioware essentially rebooted the series, which is really fucking weird considering its literally just the second game in the series. Make the series, instant reboot.
Without spoilers, the game quite literally takes everything that ME1 accomplished, removes it through some half assed reason or other, and then has you redo half of it with a new plot line, new enemies and very different gameplay. A big fat reset button is hit on the story, the characters, and even the player character.
That being said, it does provide constant little nods to ME1, through the appearance of side characters who are like "Hey, you did that thing last game, I'm going to say hello now", increased starting resources, and slightly different dialogue lines dependent on the 'choices' you made previous game.
None of it is actually relevant to Mass Effect 2 and the story it is telling though, nor to Mass Effect 3.
ME1 is IMO the best of the series. Which you will prefer depends greatly on your taste in Sci-Fi and gaming. Shamus Young has done an extremely in depth and highly spoilerific analysis of the entire series, and I'm going to de-spoiler it and provide a very verbose coverage of some of the main points here for you.
Mass Effect 1 is details first Sci-Fi. The world has rules. Those rules are followed fairly consistently, from everyone needing to wear space suits in a vacuum, to what Mass Effect fields can do and how they work. A lot of attention to detail is paid, and consistent throughout the story. Everything has a reason it is happening, it is understandable and normally not too BS, and that reason is liable to pop up again in another circumstance or story in the game world. There are a ton of optional quests and characters that exist to give life to the world, and entire core sections of the game can at times be dedicated to fleshing out the world and making it feel like a living, functioning world, rather than providing a mechanical challenge of any sort. Almost any question about the world has a thought out answer, from how Mass Effect powers works, interspecies politics, military chain of command and tactics for space battles, how the FTL functions and what its limitations are...
Its sort of like Star Trek. There's a lot of time spent building the world and getting immersed in it. Gadgets and gizmos have rules, and to get around them an explanation must be given. Rule of Cool is almost never used. ME1 is more consistent in following its rules than Star Trek is too, though both offer detailed, if not always realistic, reasons for things happening.
Mass Effect 2 is Drama first Sci-Fi. The rules of the world, internal consistency, logic, and details are all irrelevant and quickly discarded. What is more important is the drama; the character interactions, the fights, the tension of that moment when all little plot holes and details are ignored. The world works in service of the story, whereas in details first the story is often in service of the world. Many of the details from 1 are carried over... Then promptly ignored by the game itself whenever convenient.
Its more akin to Star Wars. We don't need to know why the force works, exactly what rules it follows, what it can and can't do. We don't need to consider the logic of Luke being able to to 'sense' the location of the Death Star's exhaust port and hit it dead on, or why the missile fell down at that point when normally they fly straight. What matters is the drama and tension in that scene.
Another example offered by Shamus himself was with C3PO. In Empire Strikes back, he's disassembled, and the characters must find him, put him back together, and then talk to him in order to learn of an Imperial ambush. This is very drama first. Think about the scene. Why did they need to rebuild C3PO. He has data banks. Couldn't they have just plugged in one of the gadgets they were carrying and watched a recording of what happened to him before he died?
Of course, that wouldn't have worked in Star Wars. The entire movie is dedicated to keeping that drama, and we are positioned to think of C3PO more similarly to a human character that was just resurrected, than as a simple machine to be manipulated for information. His strengths lie not in the details of how he works, but in the drama he provides as a character.
Neither is inherently better, but both are completely different experiences, and which one you overall prefer will likely determine which game you prefer, though it is widely accepted that ME1 has by far the better story, and better world building, while ME2 has the best rendition of the world's characters [Funnily enough, the strengths of details vs drama].
Gameplay wise, the two are also quite different.
Mass Effect 1 is a complete hybrid game. Think Morrowind. Real time action mixed in with RPG stats. Sometimes its clunky. Hell, a lot of the time it can be. However, IMO, it also has its strong points.
Casters in ME1 are true casters. Ability alpha strikes, debuffs, DoT... Your weapon is always usable, and you can still use any weapon, but you won't be 'trained' in it by being able to put points into anything but the pistol, and sometimes one other class specific weapon. What this means is that you won't get the weapon abilities [E.G: The assault rifle gets an ability that allows you to have near perfect accuracy and near zero heat buildup for a certain period of time, allowing for long, sustained, highly accurate bursts of fire to take down tough or distant enemies], that your weapons deal less damage, and that their 'accuracy circle' that determines their spread is far larger, and expands far quicker. And Sniper rifles sway much more too. In return though, they get a huge arsenal of Biotic or Tech based abilities to use, with a mix of utility and direct damage. There is no 'mana' to speak of, so you can cast all of them just fine. They all have their own independent cooldown, so it is always possible to alpha strike, and always entirely up to you what abilities you'll use, when, and where. And there are some parts of the game where these abilities are a true lifesaver, and when enemies get them they can really mess you up.
Soldiers are pretty basic soldiers. No tech or biotic abilities, but they get all weapon abilities, a lot of health and health regen, and are able to level up every weapon to its fullest. There are also hybrid classes that get a bit of both.
All weapons have unlimited ammo, instead relying on heat buildup and fire rate to limit your damage output. All weapons and armour are also able to be modified by various 'mods' that you can acquire as loot, or purchase [Loot is 100% automated upon killing an enemy]. Some increase damage, some decrease heat buildup, some make your bullets explode. The same weapon with a different set of mods can behave completely differently [For example; Sniper rifle with exploding rounds, and a double damage increase barrel mod will deal very high damage with some knockback and small AoE as well, however can only fire a single shot before overheating and needing to rest to cool down. The same gun with toxic rounds and a double cooling improvement mod will become a weapon unable to instantly kill with a single shot, but capable of taking multiple shots in quick succession, and often killing with a single shot thanks to the toxic DoT].
On the downside of the equipment, your inventory has a horrible interface, gets cluttered very easily, gets overfilled very quickly, and the gear is not at all balanced, with classic RPG stat differences; a couple of really amazing types of each weapon, and a lot of shit ones, and then a couple that are great in one aspect but terrible in the others, and even with the mods some are just go-to for how great they are on certain weapons.
Combat occurs with essentially infinite range; I've sniped 'boss' enemies to death from a kilometer away without ever being in real danger. At the same time, some encounters will force you into close range for the fight. Verticality also exists, and you can end up high above, or down below, enemies in some stages or areas.
You can take cover behind objects, however it is often not necessary to do so, as you have a fairly reasonable health pool, and certain classes regen that health over time. You can use medigel to heal your party and resurrect them too, and some levels are even designed such that you'll be constantly on the move, rather than hiding in cover, to give them a certain feel. Other levels are the opposite.
Transport around the galaxy is just selection from a map, though the map does have secrets you can find if you highlight over them. Non-core story planets are incredibly bland Procedural Generation terrain, with cut and paste 'bases' to explore, however are free roaming within a large but limited area, and do have 'secret' items to find too.
The Mako vehicle is your main mode of long distance transport on planets. It is incredibly tanky and bulky, having easily 100 times as much HP as your tankiest character even end-game. Its weapons are very powerful, it is capable of repairing itself over time at the cost of 'omni-gel', which is acquired by melting items you don't want, however it is disabled while doing so. It also has auto-regening shields, where the majority of its health comes from. It is, however, difficult to control, being rather touchy with the steering, using tank controls, and adhering to physics a little too well with very bouncy suspension, resulting in a few rage inducing easy flips that you can't recover from.
Mass Effect 2 is your modern 'hybrid' game. It is a fairly standard third person shooter, ala Gears of War, without any real stand out features in that department. You have very little health, and are almost constantly stuck in cover. Some classes can get around this in some circumstances, but even then the game throws enemies at you that negate that ability, and on higher difficulties it becomes very difficult to pull off an aggressive push out of cover and survive.
Guns are all pre-determined with their own behaviour, and by and large a pretty straight progression from average to good, with a couple of exceptions. You have no inventory, only a loadout. All guns now have ammo that must be collected, and they have to reload. You also have "Heavy" weapons that use a special kind of ammo, and can have a few different effects depending on the weapon.
Abilities are near useless on any difficulty above normal. Even on normal, almost all of your damage as a caster class is going to come from your guns. You are limited in which guns you can use; casters only get the pistol and SMG, soldier gets everything except the SMG, and hybrids get the pistol, SMG and either the sniper or the shotgun. And this is hard limited; you cannot equip or use any other weapon than the ones you are allowed to, until mid-late game when you are allowed to select one additional weapon type to use [Or an uber version of a certain weapon type you can already use if you are a soldier or hybrid]. This does mean, however, that the guns all control tighter and more like a standard 3rd person shooter experience.
Enemies now have 4 types of health, rather than 2; Health, Armour, Shields and Barriers. Not all are present on each enemy; on normal, most except bosses will have only health. Health is vulnerable to everything and suffers full effects from all abilities. Armour is vulnerable to slow firing weapons, takes increased damage from warp biotic attacks and fire based tech abilities, however negates all effects from abilities [I.E: Biotic lift will not lift an enemy with armour, only damage the armour]. Shields are vulnerable to fast firing weapons, and take increased damage from electricity based tech abilities, and negates all effects from abilities. Barriers are vulnerable to fast firing weapons and all biotic abilities, and negate all effects from abilities.
On hard and up, every enemy has armour, shields, barriers, or a mix thereof. Seeing as all of them negate the effects of abilities, you can see why all bar a few abilities are largely useless. On normal and below, however, it is just faster to give them a half second of fire from your SMG and they're dead anyway, no need for abilities.
Abilities also now all have a shared cooldown; use any ability, and all your abilities are disabled until the cooldown is up. This means that even on a caster type class, you'll really only have one ability you'll level up and use, as the others won't be as strong, and thus just won't be able to be used.
SOMETIMES you can find a situational use for multiple abilities, and sometimes they can be helpful against bosses with large amounts of a certain defence, but generally they're a liability more than an asset, unless they self-buff.
Also, ammo types are now a toggle ability that you turn on and off.
All fights also occur in cover, which is omnipresent, and your health regens automatically after not taking damage for like 3-10 seconds - damage detection can be pretty shit sometimes. All fights are very close and short range, and only a few make use of different height levels.
All levels are now handcrafted, however because of this there is no real exploration to do in a level. This has been relegated to the galactic map, which you must now traverse by clicking to 'fly' your ship through space, and making sure you have enough fuel to get where you're going. You also now mine for minerals on various planets in order to buy upgrades on your ship that increase your stats like weapon damage, since we've got to keep that in the game but we don't want to give you too many options when levelling up.
Your main form of long distance travel in a level is the loading screen, which will transition you between small, enclosed areas so that you don't have to travel by foot since the vehicle in this game is DLC only, and only available in a handful of missions even then.
The vehicle is the Hammerhead. Its faster, has standard move controls rather than tank controls, is more responsive and hovers so that you can't flip it. The downsides? It has a peashooter for a weapon, with auto-tracking projectiles that aim themselves to miss more than hit because they target the wrong damned enemy and you have no reliable way of making them target the one you want, and it has less health than your main character on foot - about a second of taking fire will make it explode. Oh, and a lot of your enemies are hitscan and relatively long range, and the ones that aren't will kill you with a single hit from their attacks.
The hybrid part of the game comes in with you 'leveling up', and being able to select a small upgrade to one of your abilities.
Also, rather than having to invest level up points into your diplomacy stats like in ME1, it is based 100% off your 'score' in paragon or renegade - the two moral alignments in the game - and further actions along each path are unlocked by taking the earlier actions in that path to build up that score {This was also semi-present in ME1, with later levels of each diplomacy stat being locked off behind a certain Paragon/Renegade value, so this is in some ways actually an improvement}.
If I were to make my own comparison?
They games are like the Star Trek movies. The new JJ Abrams ones are riding on the popularity of the older ones to draw in fans. You don't need to know anything about the old movies, or the series at all, to watch and enjoy the new ones. There are a couple of nods back to the old movies in the new ones, but that's about it. Additionally, the new ones are much more flashy action and lense flair and explosions and fights and drama, while the old ones tended to be a bit slower, more details focused and consistent, and not quite as flashy.
Both have their strengths, both are worth watching and enjoyable on their own merits, though IMO the New Trek less so, both also have their weaknesses. Which one you'll prefer depends what you're into in general.
