After struggling to make the combat system of Skyrim to be any interesting compared to The Witcher 2, I decided to reroll character and made a female Breton. They have a rather small frame compared to the other races, and that suits a sneaker just fine. My first toon was a female Orc, also rather stealthy but I spent points all wrong. But the "berserk" shout was quite simply insane. A full frontal two handed warrior is also quite effective and entertaining in this game, but I would still use light armor, as sneak is too important and fun to give up.
I have a great tip for you guys on how to get a sneaky character right from the start, regardless of racial choice.
(Optional) When escaping capture, at the bear, just face a wall and press autorun "c" on PC, and wait while your sneak ability pass 20. You could wait until it hits whatever number you want, really, but I started out with 15 and decided that 5 "free" points was enough for me.
(The Iron Mine) When running down the mountains, just past the "class stones", there is a small trail that leads up to a mine on the right hand side. There is an alternative entrance to this mine closer to the city, but I would suggest using the "main entrance" for this task.
Now, after going to town with your escape buddy, dolly up your gear at the smiths house, do his bidding and get yourself some easy Smithing levels. Sharpen your blades, temper your armor (always light, heavy is just pointless in this game).
Head for the main entrance of the mine, and start sneaking. Try to kill everyone stealthy in that cave. First off, pick up the burning torches on the walls as you pass them, darkness is your friend. Watch out for chimes and traps, as they can alert nearby enemies. The first couple of Bandits you encounter, just stand in the shadows and wait until one of them leaves, then kill the other while he is sleeping.
Wait below the stairs in the water line for the other to come back, and backstab him while he is studying his companions corpse.
This is how far I will "guide" you as a stealther, but one last tip is to use the Bow to attract attention without being discovered. Shoot an arrow towards the spot you want the enemy to go to, and use the distraction to make a kill, or place yourself in good position for a stealth kill.
Each stealth kill will give you a point or more in Sneaking, at least at the start. After getting 5 points from the sleeping bear, choosing the Thief stone, and clearing the Iron Mine with all stealthy kills, I had 43 Sneak. Not too bad after 1 hour gaming, and 15 sneak to begin with. I also recommend Breton (25% magic resist+shout), Dark Elf (50% fire resist) or Orc (Berserk) because of their exceptional racial abilities. Orc is easily the best melee fighter in the game because of Berserk, even for assassins.
PS. Use double swings (right & left mouse button at the same time) if you're dual wielding in open combat, the DW power attacks are quite effective, and once you pick up the 25% less stamina use it's a fight winner.