I think you're really the only one to decide which would be best for you. Now w/ Burning Crusade out, the only thing that seperates alliance from horde are the racials. Take a look on the WoW site and see which ones would best fit you. Then you can maybe try testing out different classes up to a couple levels and see which one is best. I re-rolled a Blood Elf warlock, but that's just me.
You can't change the character class you start out with. That is if you choose a class and get to say, level 40 and then want to switch to another class at the same level or change your appearance or name, you can't do that, although you can set up multiple different characters so that's not really a problem. What you need to find is what your playing style is and you can only do that by testing each class as vLm said.
In my own case I went for a Druid. They are not the most powerful casters in the game but they do have Starfire and Regeneration and are the only class apart from Shaman's who can shapeshift which can come in very handy! This let's you perform dual roles as either a bear, which gives you warrior like armor and strength or cat which is similar to the Rogue in that you can stealth whilst moving and your damage capability is pretty awesome. Then there is Aquatic form which let's you not only swim faster but you can stay under water for as long as you like which helps with a number of quests and can get you out of some tricky situations. All together there are I think, six different forms you can take. Bear, Cat, Travel Form (basically another cat that moves faster), Aquatic, Moonkin and Tree Of Life. there is also Dire Bear form but since it looks exactly like the ordinary bear form I haven't counted it. I can do five at the moment.
Druids are also great healers and have the best buffs in the game. So...a well rounded class, not the best at any one thing but probably has the greatest range of abilities out of all the classes.
I also have a hunter. Hunter's can probably solo better than most classes because they have the big advantage of being able to have a pet which fights along side you. Most of the time you can send your pet in to attack close up whilst you fire off shots from your bow or crossbow from a distance. Hunters can also wear mail armor from level 40 up which is another big advantage. Druids are limited to leather and cloth until much later levels and even then they can only wear certain types of high end leather such as dragon scale which works like mail.
Rogue's are another good class especially early on because you can level up pretty quickly. Rogues have the ability to stealth whist moving and so can sneak past most mobs to get to your goal and complete quests. They can also deal a lot of damage very quickly if needed although they can't take a lot of damage so it's best to strike quickly and then get out. Their other big plus is the ability to pick locks. However, this is tied into your current level. You can only maximise your lock picking to five times your current level so if say you are level 20, you will only be able to pick locks to a maximum of 100 skill. This is pretty useless as it means you can really only open things like bronze lock boxes and footlockers, neither of which contain anything great. It won't be until you get up near level 40 that your lock picking skills become in demand, but once they do you can make quite a bit of money opening things for other people
Anyway, there's a few idea's to be going on with. Perhaps others can add to this ?
PvP is great if you want a lot of action but it does make quests a big pain in the ass, especialy if you have to venture into enemy faction territory to complete it because they will be all over you like a bad rash! Still it can be fun and does add a certain edge to the game. Me...I prefer the quiet life of Darkmoon Fair. You can still PvP if you want but it has to be consentual on both sides and of course you can still Raid.
Anyway...whatever you do, have fun...it is a game after all, some people get way too serious over it.