Unfortunately I can't see your pet collection in your profile, (it tells me you have no pets). There isn't really a perfect team, though, and a lot of it is trial-and-error. Some people believe that certain pets are more powerful than others, (or even overpowered), but I wouldn't base decisions off of what is most-powerful at any given time, as they are still adjusting balance issues and etc.
As Grenouille mentioned, having a pet that can heal can be very effective. I leveled a Disgusting Oozeling from level 1 to 25, and I find it's Absorb ability, when combined with Corrosion, to work very well against all types of pets, with the exception of dragons.
Using a pet that is strong against Beasts and Critters can be useful initially, and can aid in training your less-effective pets. As an ex-Pokemon junkie, you should be happy to hear that training can be very similar. You can place a weaker pet in the lead, have him participate in at least one battle, and then switch him out for a stronger pet to finish the fight.
Another good method is to finish the majority of a fight using a strong pet, allow him to be killed, and then finish off the battle with a weaker pet. The weak pet will gain a great deal of exp and level very quickly.
Initially I would recommend that you simply follow the battle pet quest chain. Fighting the pet battle Masters will gain you a great deal of exp for your pets, and lead you into areas of appropriate training level.
Edited by Klinny on 9/30/2012 7:22 PM PDT