I saw a guide where some guy wrote about what race each class should choose, I felt kind of sad when I saw it (no offense) but I have really other opinions so I try to make a guide from the perspective of a quite experienced wow player. Now on to the guide!
Mage: Mages should chose human as alliance. Perception is a really good talent, a human frost mage will kill almost any rogue with equal skill and gear. It makes wonders and could often be the difference between win or loss in arena. Gnomes are ok, to escape a snare could get handy but not as handy as perception. Hordes should take undead. Gives you the upper hand against fear, it is just, true.
Warlock: Warlocks choice as allliance is also human, to see a rogue that you just saw entering stealth trying to sap could be the difference between win or loss in arena. Just choose human. As a horde it's also clear, undead, an extra way to stop fear is really nice, can also make the difference between win or loss in arena.
Priest: Really, the same as with Warlocks and Mages. Human and undead, their racials can both make the difference between a win or loss in arena. Just that night elves is quite nice as priest. Being invisible will confuse your enemies indeed. Take what you feel you need most if choosing alliance, detect hiding druids and approaching rogues or to be invisible and wait for people to come and let them think ''omgz haxxor hiding priezt lulz?''.
Rogue: Choose undead as horde since you will have a problem against sl/sl locks and I know it's almost impossible to beat an undead Rogue as a lock. In pve troll is better but the difference is not huge. Some people mention orcs but well, their stun resistance is 15% of what you already have, not 15% pure stun resistance. So if you have 10 stun resistance playing an orc will yield you 1.5% extra stun resistance. Their damage increase skill is good against none resilience targets and probably for CB>evi combo but meh, they can work, I would choose undead but it's really up to you. As alliance, human of course, gnomes could work but I prefer having the controll in arena and being able to sap that rogue before he even see you and kill that hiding resto druid. Gnomes will be able to, escape frost mages, really can't find their racial better than that.
Druid: Guyz, NE and Tauren, omgz! Hard choice ^^
Hunter: I have found night elves to be the most effective. Get a cat as pet and you can hide really nice. As a horde it's a bit harder, I haven't found blood elves arcane torrent effective so that makes it easier. Tauren's warstomp is nice indeed. I think I would choose orc(extra stun resistance, remember, it's not a 15% extra resistance, it's 15% of what you already have) or tauren(warstomp and some extra hp) for pvp and troll(nice atack speed) for pve.
Shaman: You have no choice as alliance . As horde I would really say it doesnt matter alot. Taurens got their warstomp which is just a small stun, and some hp increase, nice for resto shammies in pvp. Trolls got attack speed increase which is nice for pve shammies that go enhancement. Orcs also offer some nice burst damage and could be fun to play so, choose what is coolest.
Paladin: Human as alliance, perception is really good as I've said alot of times ^^. No choice as horde. Nothing to say more than the dwarven racial can't beat the human one.
Warrior: As alliance, take human for perception. Actually, night elves would work nice to, 1% more dodge is better than nothing for a tank and shadowmeld is really confusing in pvp. So, it's the same as for priests, take what you want, controll those nasty druids and rogues or be stealthed. As horde, take taurens for pve. Their hp bonus is nice indeed both in pve and pvp. 500-600hp it is for a normal pvp warrior and probably 700-1 000 hp for a normal tank, and warstomp is cool. But for pvp only I would choose orc or undead. Undeads got the upper hand against fear but orcs got their damage skill and stun resistance. An arms warrior will have some and the increase will be noticeable. I would go with orc or undead for pvp.
Thanks for reading this guide! I hope this helps you, feel free to say what you think.
Thanks and good luck