In the end, what kind of pet to choose is a very personal choice. Aside from the obvious issues of style and looks and cute names ("Hello Kitty"), you need to take into account the type of playing that you will be doing.
Another thing to decide on is how many different pets you want to keep. Remembering that they all take time to level, you don't want to have to spend a bunch of time leveling a pet that you will use infrequently anyway. You can buy space for up to five pets.
Lastly, you will want a pet or pets that match your Talent Specs. The pet you choose can be affected by the talents you choose, so you want to match the two as much as possible.
There are three main classes of pets, based on the "Talent Tree" that they possess: Ferocity, Tenacity and Cunning. Ferocity pets will have higher DPS, and their talents will also increase yours. Tenacity pets have higher Stamina and keep aggro better than other pets. Finally Cunning pets balance the best of both, and are flexible enough to work in most or all situations.
The best approach to picking a pet is to compare your own Talent Tree to that of the pets' trees, and decide what combination will work best in the type of scenario you will be working in. For instance, if you are Marksman spec, the you will be dealing fairly high damage compared to someone with Beast Master spec. You will also be creating a lot of Threat, and you run the risk of stealing aggro from your pet. This means that a Tenacity pet will help keep the mobs off you.
However, if you will be doing more raiding than questing or grinding, keeping aggro will be the job of the Tank, not your pet, so a Ferocity pet is called for in this case.
On the other hand, those with Beast Master spec don't have the threat that Marksman Hunters do, and can use a Ferocity pet without much fear of stealing aggro.
Cunning pets are decent for Battleground situations where conditions might change at a moment's notice. They don't have all the DPS of a Ferocity pet, nor all the Armor and Stamina of a Tenacity pet, but they are well balanced and have some other options that can help a Hunter stay alive in a PvP situation.
All that being said, it bears (ha!) mentioning that pets are a lot better than they were before the WotLK update. Almost any pet will be playable under nearly any condition, and usually all you will need to do to succeed is to change your strategy a bit based on whatever strengths your pet has. These various strengths will be explained in future posts...just check under the "pets" category.