This is my first time playing a hunter. People say its fun and its the fastest leveling class there is. So which race is the best for hunter class?

Well NightElves get the dodge and bow bonus while orcs get the pet buff. If you add in Shadowmeld for NEs I think they get an edge for PVP oriented marksman type hunters. Orcs are great BM hunters though and the stun defence is always good in PVP.

It all depends on your play style as you play your character. But once you level it to 85 or any level for that matter you can put down more money for a race change, sex change, and faction change.

If your playing Horde:
Tauren hunters have a stun that allows you to get away from tight situations along with a health buff in PvP.
Orcs have a nice stun mitigation, and a racial such as bloodfury which increases your dmg for a short time and can be used along with trinkets.
Blood Elves allow for a great silence ability during PvP so the opposing player cannot cast a spell for a brief amount of time.
As for PvE, a Troll would be a nice race for it's berserking which increases attack speed for boss fights.

With the new expansion: Goblin hunters can be exciting to play for PvP and PvE, if you like actively pressing keys/clicking you can use the goblin rocket jump, this play style does require some different micromanaging is all.

If your playing Alliance:
Currently with the new Cataclysm expansion, Human hunters provide an extra trinket slot so you can customize for better PvP. They have a racial ability called "Every man for himself" which dispels a movement impairing effect where as other races have to have a trinket.

If you don't like Player vs. Player (PvP) you can pick a dwarf because of it's minor +skill to guns for better hit chance.

All in all it's best to pick what you feel comfortable playing, you'll learn to love and hate from your mistakes. Whether you want to play as some big juggernaut player or tall and lanky, or even short and stout. As you play you'll figure what is best for you, so I'd recommend which best appeals to you the most, and which will let you have the most fun.

Orc, goblins are interesting also, but orc is still king

Depends on your play style.

Alliance:
N.Elfs are agile, good at range and combat. base pets pets are as well, and have tricks.
Base pets: Spider, Panther, .. and Bird i think

Dwarves are sturdy, better at melee then range. Base pets are heavy too, mix of melee and tank
Base pets: Bear, Boar, unknown

Drainai unkown
Base Pets: Uhhh Razormaw.. thingys...

Worgen unkown. Cata sucks!
Horde
Troll similer to N.elf statwise.
Base Pets: Thundersnake, Tallstrider, unkown

Orc: High strength, good melee damage.
Base pets: same as Troll

B. Elf high agi with the str to back it. High damage.
Base pets: bloodstoders, unknown.

Goblin: unkown Cata sucks!