For an easy-to-play profession to start playing WoW with, I would suggest a Hunter. Later on as you start new toons and try out different classes and races, your Hunter can serve as your farming machine, looting gear and whatnot to pass along to your lower-level alts. This worked out very well for me. Hunters are ridiculously easy to solo things with PvE.
Paladins are also an excellent choice for a solo class. Putting your talent points primarily in Protection and secondarily in Retribution gives you tanking abilities plus a little DPS edge, enough to take out mobs at a decent rate on your own. My Paladin is just such a mixture and he does very well in most situations. When I'm finished grinding him up I will switch him to Holy/Protection, but until then, Retribution serves best for leveling.
Warlocks are fun to play and can be very nasty in PvP. Putting your talent points in the Affliction tree is a popular way to go for PvP. It also helps you in PvE as you can slap several mobs with Siphon Life (a nice instant cast), thus giving yourself a steady influx of health as you do your thing. I tried Demonology in my middle 30's and have decided that is best to do with a 50+ Warlock, and that is just to gain the Felguard minion. Even though Blizzard hit 'em with the nerf bat, they are still nasty in PvP.
Mages start off pretty weak but if you want to own in the damage department, roll a Mage. If you have any doubts, then watch a Frost-speced mage handle a huge crowd of mobs on their own with barely a scratch to show for it. Mages can achieve insane DPS and usually end up being the one all the mobs go after in an instance...so therefore, be prepared for alot of evasive manuevering.
On the Alliance side, I have all of the classes and races represented in my toons. For a Mage, I think Gnomes are the best choice. For a Warlock, either Human or Gnome (your only choices anyway, heh). Draenei make great Paladins due to their racial ability, though a Human or Dwarf will do just fine as well. Night Elves are a slick choice for Hunter since they have a racial stealth ability....add that to the Prowl ability you can teach a cat pet, and you have a nasty surprise for your enemies in PvP ( I have used that to great effect in Warsong Gulch...camping flags in stealth). Just about any race will do for warriors, though I prefer Humans or Dwarves. For a Priest, either a Human or Draenei, though again any race will do fine.
I'm a huge proponent of Paladins being main tanks for several reasons. First and foremost, a properly-speced Paladin will have more armor than other classes. The Protection talent tree gives a Paladin some awesome tanking abilities, not to be overlooked nor underestimated. Secondly, the wide array of Seals and Blessings at a Paladin's disposal makes him an excellent choice to throw headlong at a crowd of mobs.
For example:
A Paladin can keep his mana constantly refreshed by firing up a Seal of Wisdom on himself. Every time he hits a mob, there's a chance of gaining X mana. Alternatively, he can judge mobs with the same seal and give everyone who hits that mob a chance to gain x mana when they hit it with melee, ranged, or spell attacks. He can then re-cast the Seal on himself, since that version grants more mana per hit. He will need it to spam his holy spells.
The same Paladin will have Righteous Fury cast on himself, drastically increasing the threat his holy spells create, keeping aggro centered on himself. He then can spam Consecrate, an AOE holy spell, keeping all the mobs in his area occupied with him while others work them over.
If in the course of things some mobs break off and go after a Mage in the group, the Paladin can cast Righteous Defense on that Mage, bringing up to 3 mobs attacking that Mage right back to him. I have saved the skin of many Mages and Priests that way. Works like a charm, and has a long range.
A Protection-speced Pally has awesome defenses and can take a beating right alongside a warrior or druid in Bear form. The bonus for the Pally: he can heal himself more quickly than a druid in animal form can, who has to shift back into humanoid form to cast a spell; and of course unless he drinks a potion, a warrior depends on others for healing. A big downside to a feral Druid shifting in and out of forms: he loses all of the Rage (Bear) or Energy (Cat) he had previously when he returns to animal form. They have to build back up again. Points in the Restorative tree can help with that, but it still sucks big-time if you ask me.
Last but not the least, a Paladin has a wipe-preventing power called Divine Intervention. If things look grim and everyone is either dead or about to croak, a Paladin can cast this on a group member with rezzing ability and in doing so can prevent a group from wiping. When he uses Divine Intervention it kills him...however, the recipient of the spell is invulnerable to all harm for 3 minutes, and will lose all aggro. This is perfect to cast on a rezzer. I had the chance to use it once (Maraudon in fact), and felt like a million bucks.