Hi, and welcome to the hunter class!
Watch out for Dragonhawks - they look awesome, but they have "weak caster stats" and don't make the best pets. See Petopia at brashendeavors.net for more info (go there - killer pet site -study it).
The other poster is right about the red lynx type cats. They will be a pain at first because they'll be a bit low level, but they should level up to you quickly. They are the only red cat I know of, and look awesome.
That said, the boar actually is the "best" low lvl pet for grinding/leveling. Your best bet is to go to NW silvermoon (iirc) and find the teleport to the Undercity (UC). There you exit the city and go north to hte zepelin tower. Take the one to Orgrimar. Rt click the goblins to find which is the zep to Org and which goes to the jungles of grom'gol and STV.
At org tower in durotar, find a pig and tame it. THis may sound like a major undertaking, but you can do it in less than 10 minutes. And if you have some money, you can train other weapons in Org - if you want to. You can only learn to use certain weaps in certain cities.
Why a boar?
They eat anything; easy to feed.
They have good hp and ac; they tank well.
They have CHARGE - the only pet before lvl 32 that can go to target FAST. The convenience is amazing - you don't have to wait for pet to charge to target. The time saving alone times thousands of fights is worth it.
Charge = the boar holds agro better (it has an attack buff on his next hit).
They get bite and gore, so they can do okay dps.
Note: gore causes focus to get used up fast. Consider turning it off til you get a talent that grants faster focus regeneration (one in BM tree, one in MM tree). Also, turn CHARGE off when in a group - it can cause the boar to sometimes misbehave and attack mobs he shouldn't.
If you don't wanna do this - any pet will work - even a wimpy dragonhawk. And of course, you can change pets as you level up. Study petopia and see which pets really appeal to you. You may want to tame the rare, black dinosaur. You may want a ravager (but going to Dranie lands to get one is harder now - guards on the boats). Mostly pick one that you will like. The boar really is great, but again, any pet - even a stupid crab - will work. GL!