Horde is the better faction. It tends to have fewer jerks, idiots, and immature players. Alliance players will try to tell you that it’s a wash these days, but they are either lying or delusional. Horde isn’t free of jerks, idiots, or the immature, but when I log onto one of my Alliance alts I usually run across someone behaving far worse than I’ve ever seen on Horde side. If I weren’t already established on my server I’d roll on Cairne to check out that SDMB guild.
Cataclysm, the next expansion, is only a few months away, and it will overhaul “old-world” content. The power levels of all of the classes are almost certainly going to shift around a lot, and I wouldn’t trust anyone who claims to be able to predict who will come out on top. You can have up to ten characters per server and fifty across all servers (and they don’t charge you extra for them), so go ahead and try out different classes. There will be some new race/class combinations available in Cataclysm and two new races, but racial abilities are honesty really minor, and you can change your character’s race (for real money) if you really really want to.
If you only want to have one character, bear in mind that only druids and paladins can fill all three roles (tank, healing, DPS). This is important to some people, but I’m perfectly happy with my main being a mage (only DPS). I suggest you start with whichever class has the archetype that most appeals to you.
As Yllaria said, gathering professions are excellent for new characters. Many players with high-level characters will pay handsomely for the raw materials they need to power-level the crafting professions (blacksmithing, jewelcrafting, etc.) on their alts. A stack of copper will fetch several orders of magnitude more money on the auction house than you get from doing quests in the early zones. Mining and herbalism come with the “find minerals” and “find herbs” abilities, respectively. These abilities act as a sort of radar that makes mining and herb nodes show up on your mini-map, but you cannot have both of these radars active at the same time so getting both isn’t the best idea. Tailoring and enchanting don’t rely on a gathering profession for material, but enchanting is prohibitively expensive for a new player. Mining and tailoring make an excellent combination for a new mage, priest, or warlock.
The other side of this coin is that a lot of low-level gear on the auction house is a rip-off and priced above what a new player can be expected to afford. Don’t worry, though; this game is very easy and you can get by just fine with only the gear you get from quest rewards. Getting bags off the auction house (not from NPC vendors) is a good investment. The best bang for your buck for a new player at the moment is probably still the “netherweave bag” (the baseline crafted bag from the previous expansion) with 16 slots each. The “frostweave bag”, the baseline crafted bag from this expansion, has 20 slots but cost about four times as much the last time I checked.