A few suggestions:
Orc heavy armour+Blunt weapons is always fun. Smashing your way through anything. Combine with enchanting, armourer, and restoration for ridiculous armour buffs and the ability to shrug off hits with a quick restoration spell (this does require a little investment into magicka away from the health and stamina, but if you only plan on using restoration, it shouldn't be too great a drain).
Stealthy archer. Play if you want to be able to break the game and make it your *****. At first you'll feel a little underpowered (it shouldn't hurt too much to invest a little in one handed weapons, as to give you something to fall back on when the enemy closes in). Invest in illusion to become even better at sneaking, invest in conjuration for handy distractions, and invest in pickpocket/lockpicking if you wish to be a theif. Wood elves seem to best suited to this, but with enough investment, any race could become this unstoppable arrow-flinger. One of the great things about this is you can add your own spins pretty freely, as all you really need to invest in is sneak and archery, leaving you a lot of space to customize as you see fit.
If you plan on playing as mage, start as something with magic skill boosts, for gods sake. At early levels, magic is pretty hard to wield on it's own, such is it's reliance on magicka, and the relative weakness next to simple melee skills. It's rewarding and in depth, though. High elves are the best for this. Dark elves are good for sneaky types with magic thrown in, especially destruction. Bretons are good for adaptability, and Redguard can make for surprisingly good battlemages, as they come with buffs for one handed/sheild, and destruction.
Hope it helps!
EDIT: By the way, if you're planning on getting dawnguard, find somewhere out of towns to sleep, don't enter towns at night unless you have to. Vampires get in towns at night. You can kill them, but only if you're there. I've had vamps come in on the other side of whiterun from me and kill belethor. Usually, you can save people with a bit of savegame time travel, but it's best not to take the risk of losing valuable merchants and NPCs.