A good combination I've found is a warrior-mage hybrid.
Race: Dark Elf/Nord - Dark Elf has amazing resistance to Fire, and can summon a ghost to help deal with most early enemies. Nords have high health, a powerful daily shield ability and a very powerful frost touch spell that kills most early enemies in one strike. Nords also have decent resist against frost attacks, making certain spellcasters and monsters easier.
Sign: Lady or Thief. The Lady is good because of the added health through Endurance, and additional early mana regen through willpower. The Thief is good because of its additional 10 to luck, which affects every single stat and ability in the game in a positive direction (and effectively grants you 10 levels worth of luck increases in a single move), and for the agility which reduces the likelihood of you getting staggered by enemy attacks, which is very nice for early levels.
Major Attributes: Strength, Intelligence - Strength for additional loot-carrying and additional weapon damage, intelligence for higher initial magicka reserves, making spellcasting more viable.
Skills:
Blunt/Blade - Whichever you prefer, but there are more rare and powerful swords than maces or axes.
Heavy Armor - Your strength permits it, and it lends you much better protection, meaning that touch spells become a more viable option.
Block - Unless you're going for two-handed, block is a must. Makes your shield last longer, absorb more damage and increases the likelihood of staggering enemies upon blocking.
Destruction - Damage output to compliment your melee attacks.
Alteration - Shield yourself, feather spells, unlocking doors and chests, elemental shields (grants protection from an element AND a boost to armor class), water breathing and walking. One of the most versatile spell schools in the game. Eliminated the need for security if you train it enough.
Armorer - Keeping your equipment in good shape saves a LOT of money, and ensures that you continually train your endurance (for additional health) while having a tip-top damage output and defence.
Illusion - Not a primary skill of the build, but it can serve two purposes. First, it'll make the likelihood of accidentally leveling too fast smaller, and it has some pretty decent spells, like Paralyze, Invisibility and charmeleon for when you need a bit of strategy.
Merchantile - This skill increases at a dreadful pace, making accidental leveling less likely. Also, getting a good price for your stuff means more money for custom spells and enchantments.
Mysticism - One reason: Soul Trap. Mysticism is kind of a redundant skill with Mark/Recall being removed, but soul trap is a wonderful spell for when you get magical weapons, and will help you make good magical gear for yourself. Certain spells, like absorb and reflect can work well, by turning enemy attacks and spells back at them, but they're unreliable in the long run.
The reason we've left out Restoration and Alchemy is this: Restoration increases incredibly fast, and it shares the attribute of willpower with Alteration and Destruction. Leaving one, especially one you use a lot and is easy to train, means that you will be almost ensured of getting that elusive +5 attribute increase per level up. Same with Alchemy, only you will need to purposefully grind this. By collecting food and making fatigue potions, you can control how many points in alchemy you want (remember, for a +5 you need 10 points in the related skills), and you can sell the potion for far more, in the long run, than you could the ingredients. Eventually, making potions actually becomes a viable and useful means of extending yourself, such as making powerful health, mana and feather potions.
With a game like Oblivion it's important to know what kind of character you're going for. With a bit of playtime and experience you'll soon learn what skills are useful, and what skills aren't. The above is a good, versatile frontline sword-n-sorcery type adventurer, but is not worth a lot in terms of stealth gameplay. Still, I've successfully completed 90% of the game (even the thieves guild) with this character.
For all the touting that Morrowind is the superior game (and in many respects, it's true), Oblivion is only really flawed with its leveling system. Sure, people like to nitpick about things like voice actors, but these are superficial complaints to "justify" them not liking something that's popular. Because, y'know, having an opinion and sticking to it by the value of your own integrity is overrated. Clearly the game is not your cup of tea because they only had 17 voice actors (that's including Shivering isles, 13 without), not because it just didn't strike a chord with you.
Give the game a chance, play around and explore for a bit. With any luck, you'll see the depth of the world beneath the superficial Tolkien exterior, and have as much fun with it as I have.