To be honest, the races only have a very slight differences, and are mainly asthetic differences. As for classes depends on what appeals to you
Hunters, walocks and mages do ranged damage, hunters can tame creatures you see around azeroth and have them fighting for you. Walocks can summon demons.
Druids are an all round class, they can heal do DPS and tank, they shape shift into different form, thet can take of the fom of a lion/panther for DPS, a bear for tanking etc.
Shamen bit a of a weird class, not played one tbh so don't know much about them

They give enchants to other players to boost their stats and are also healers.
Paladins are healers that wear heavy armour, before the expansion everyone hated them.
Rogues are the stealthy class they can hide in the shadows, and ambush enemies. They do a lot of damage and use daggers and swords, but wear light armour.
Warriors are the vanilla class in WoW big weapons and heavy armour, or at the end game you'll probably be tanking, which means you'll be the one stood at the front of the fight getting the **** kicked out of you all the time
Priest, the best healers in the game. You're there to heal and will probably be one of the most popular ppl on your server if you roll a Priest. You can also do a lot of damage if you become a Shadow Priest, but the main thing for priests is to heal.
*I'm sure this is going get picked apart but I think it's simple overview of the different classes.