Level your char to 90, you will have it so much easier. Then keep progressing on the chains, you will be send to EK, Kalim, then Outland, then Northrend, then Cataclysm zones, then Pandaria. In pandaria is where the tamers with XP are for levelling pets fast to 25, the satchels with rare stones in them and some pets aswell. And a lot of wild pets... a lot
For PvE, wild and tamers, you can pretty much use any pets you fancy. Make sure you do have +50% bonus damage, 33% bonus defense is nice aswell. A few pets are doublecounters and have both traits, so they are really endurant vs tamers.
I'd suggest you read some of the guides here on the site, addons aswell will make life way easier as the default Blizzard design is..ye.. well.. blizzardy.
And breeds. If you don't know what that is, then you got that to look forward too aswell
As you defeat tamers, and continents, you unlock them. Its good XP but nothing compared to 4-7k XP from pandarian tamers. Also its way too much travel to go around. You can always boost a lvl1 against any level tamer and it will get XP if it got switched in/out upon death of another of your pets. Ofc a level 1 cant survive backline damage but not all tamers have that.
Theres a lot pets that drop from various sources other than the wild. Perhaps make a few a miniproject to try and gather