I'm getting skyrim, and I don't know much about it. I want my character to be mostly focused on magic with a huge potential to learn a lot of spells and be good at magic as soon as I make him, yet at the same time, I want him to be stealthy. It's not as important as the magic aspect, but It would still be nice to have the element of surprise. I would like to use melee weapons too, but they don't need to be a top priority.
So magic is most important to me, followed by stealth, followed by melee.
Every character can do everything. Stats just start lower for some. For a sneaky mage with mage being your focus I'd go with a Dark Elf. They start at 20 for sneak, alchemy, illusion and alteration as well as 25 in destruction magic.