Druids or shaman are a good place to start. Their classes have so many options presented to that it will give you a good feel for everything. If there's one particular thing you like from them, there's another class which mirrors it. They're presented slowly though, so you aren't overwhelmed. Paladins are easy mode. Warriors have it hardest leveling up, but, at they're best, they tear people apart. The problem is they're so gear dependent. It sucks.
Get bags. Check the auction house for them. They're very, very useful.
Pick up two gathering profession for now. I'd suggest mining and skinning. You'll be killing lots of boars, anyway. And copper is worth more than the early herbs. I've made lots of gold on the auction house buying and selling copper.
Don't leave the starting area until you're level 6. If you hit five at the last quest, go back and grind a bit. Trust me. It's worth the new spells you'll learn before leaving.
Explore. The best part about WoW, in my opinion, is the gorgeous world. Just screw around. You can get to the max level when you feel like it. Until that time, just make your own fun. While a lot of people will tell you to avoid PvP servers, I say go for it. RPPvP is good too. Sure, getting ganked sucks, but you lose out on a huge part of the experience. Plus, once you're big, you get to pay people back in kind.