With one account you get up to 50 characters, with a max of 10 per server. (there is about 90 servers to pick from)
Then there are 2 factions, each with 4 races to pick from.. Alliance and Horde
Alliance includes Humans, Night Elves, Dwarves, and Gnomes.
Horde includes Orcs, Forsaken (undead), Tauren, and Trolls.
BTW, there are two server types. PvE (player vs environment) and PvP (player vs player). On PvP servers members of the other faction can attack you at will unless you're in one of your factions "home" (starting zones). This means that if you're doing a quest you not only have to watch out for NPC monsters, but also members of the opposing faction. PvE you have to specifically enable your PvP 'flag' to fight the other faction. Both types of servers will someday be getting the Battlegrounds instances where Horde & Alliance will face off in specific zones designed for PvP.
Classes are limited depending on which race you choose, but here's the complete listing.
Paladin (alliance only)
Shaman (Horde only)
Druid (Night Elf & Tauren only)