I'd specialize in stealth, small arms, and repair right from the get-go. Also,along the way,pick up a good melee weapon,just in case (or,if you're lucky like I was,get the Deathclaw Event at the Meresti metro exit near Minefield. DCG at lvl 7).
Early on,just roam around,killing things,hacking,lock picking,disarming mines/traps,picking up EVERY piece of ammo,for use or selling,pick up all the chems,get as many stimpaks as you can find/buy,and if you have Operation Anchorage,the Steath Suit is your god. Wear that with a relatively high sneak skill,nothing will find you unless it trips on you.
My loadout by lvl 23
-Scoped .44 Magnum (Headshot kill on lone,light armoured targets)
-Deathclaw Gaunlet (First strike well-armoured foes,or a crowd)
-several pounds of mines and grenades to reverse pickpocket (For what can survive a DCG sneak crit and will wreck me otherwise)
-Combat Shotgun (For when stealth fais)
-C.Assault Rifle (Backup for crowds)
-Sniper Rifle (I forget why I still have this...Omit if you want)
When I get to the pitt,I'm probably going to replace the shotgun with the Metal Blaster, which is a laser rifle shotty. On sterroids. From Hell.
It would help to be female,so you can have Black Widdow as a perk,because most human enemies are male. Aim for Strong Back,Scrounger,Fortune Finder,Silent Running,and Robotics Expert for obvious reasons. Sniper and Concentrated Fire also help a fair bit if you use VATS often. Avoid perks that add points to skills,EXP gain, or SPECIAL,you'll get there eventually,or you just don't need it. Treat Here & Now like the Black Death. Don't rush into battle blindly;stay back at first and assess the situation. Take out stragglers and/or the most dangerous foes first. Rely on Stealth Boys early on for staying out of sight in plain sight until you get the Stealth Suit if you have Operation Anchorage. Otherwise,keep at least 5 Stealth Boys handy. If you're found out before you've made your move,go loud if you can't escape and/or hide again. With my reccomended build,AVOID ANYTHING HEAVIER THAN RECON ARMOUR,it would just be a pain and not worth it unless you get Silent Running and don't care about loot.
When levelling up skills,NEVER jack them up over 90 unless you've already found the associated bobblehead. Save often,ESPECIALLY before where you expect a major conflict to arise.
Those are my tips. That's how I run,and I only died three times. And I run on Hard mode. I feel certain it will work for any difficulty,though.