My original team choice was based on stats and strengths/weaknesses against starting area wild pets. I chose pets that had relatively high (yet somewhat even) attack and speed, as well as health. And since there are so many Critters, Beasts, Aquatic, and some Flying types when first leveling, I went with Flying, Beast, and Mechanical.
Now that I have many level 25s, I choose whichever rare quality pet I want to level up next. For the Tamer dailies, though, I pick pets that have strong attacks against the NPC's pets.
Time to level a pet varies from player to player and depends on how focused you are. If you want to take the time and capture everything, find specifically colored pets, and catch only certain qualities, it could take you some time to reach max pet level (this is also taking into consideration if you only play for a few hours a week).
It's tough trying to level a character and a pet at the same time, since it's so easy to get distracted by all the new pets to capture. I found that I had to focus on either one or the other, but I'm sure if you put your mind to it, you could pull it off.
There's no ETA on when patch 5.1 will be out, so it's hard to say whether or not you'll be pet level cap by then. I would say just do your best and play in the way that makes you happiest.