The Hunter's Pet Bestiary - This is a comprehensive list of just about anything and everything you'd want to know about pets in 1.12 WoW. (The exception of course is the respawn timers of rare mobs.)
Web Archive of 07' Petopia - This is an archive of the webiste Petopia as it existed in April 2007. Linked is 'The Big List of Pet Skills' including information such as types of pet abilities, when new abilities were patched into the game (current in-game is patch 1.9), locations of pets that have said abilities and of course ones that can be learned at the pet trainer.
This is not a completely exhausted list of general info about hunters pets and will be updated as I think of more to include!
1. Which Pet is best for me?
For leveling: At level 10 hunters gain the ability to Tame Beast, and it is generally accepted that from that point till you hit level cap you should use either a Bear, or a Boar. If you have checked out the link The Hunter's Pet Bestiary you might have seen that Bears and Boars have an increase in Stamina and Armor compared to other pets. This is very important for a leveling hunter as your pet will be your personal tank of sorts while you solo level, while you remain the main source of DPS. (Also very helpful for solo farming at lvl 60).
TL;DR Get a bear or boar as your starting pet
For PvP: The most important aspect of a hunter's pet is it's attack speed. This is due to the fact that each individual hit from a pet slows the casting of spell casters. So the faster the attack speed the more benefit to the hunter. Again, if you have seen the link The Hunter's Pet Bestiary you might have noticed they included the attack speeds of EVERY pet in the game. Pretty handy. Now, based off of this there are 2 pets in particular that stand out with a 1.00 attk speed. Those two would be the rare mob Broken Tooth, and the mob inside of the raid instance Zul'Gurub the Bloodseeker Bat. Beyond that at second place there are a handful of mobs that have a 1.20 attk speed. Which, if you plan to PvP at lower levels is your best bet. Personally I got the level 12 rare mob The Rake which is located in one of the horde starting zones Mulgore and has a reasonable respawn rate of 1 hour. There are quite a few more cats, 2 wolves, and a carrion bird that match that speed that are listed out inside The Hunter's Pet Bestiary !
TL;DR At 60 get ZG Bat, below that get a pet that has 1.20 attk speed close to your current level check out The Hunter's Pet Bestiary to find one.
For Raiding: Now for raiding you have separate needs than other types of pets. Some raid bosses have massive AoE rendering melee pets worthless, or for general peace of mind not being blamed for pulling additional mobs and wiping an entire raid. For that reason either a wind serpent for it's ranged Lightning Breath attack (MUST be set and used with a macro), or a wolf with its Furious Howl ability at rank 4 (Also MUST be used with a macro) - Party members within 15 yards receive an extra 45-57 damage to their next physical attack. Lasts 10 seconds. Now some Wind Serpents have inferior stats, but at lvl 60 the Son of Hakkar inside of ZG has good stats and has the bonus of still being able to be gotten solo. Solo Son of Hakkar video I did a variation of this with using an invisibility potion and just make a run for the bridge, then kept everything the same as in the video. As far as wolves go any wolf will work, as long as you have learned rank 4 Furious Howl. The only mob in the game that has that is the Bloodaxe Worg inside of Lower Blackrock Spire. While I have heard it is possible to do solo, I have not done so myself, so I would recommend going with a group. Now as far as the macros required for using these two abilities I still have not tested them myself, but I will update this when I have done so.
TL;DR Get either a Son of Hakkar from ZG, or the Bloodaxe Worg from LBRS. Both REQUIRE a macro set up to use their abilities so that they do not start to melee attack. (Will update with macros later)