Does it stop when they are all grown up or is that abilities? Say your pet has 255 in a stat and you manage to get it to say, 150 , by the time it is grown, can you keep training the stats or are they stuck at whatever you have them at when they reach their last growth state? I was thinking of buy a crown pet for my life, or death, but I don't have trillions of gold for snacks or a house or what have you and don't want to waste real money on a gimped pet.
Stats continue to rise until you have filled the stat bar up. But you may not need to fill all stat bars. I have pets with all damage, critical or resistance talents. Some of those may not have any or very little showing on the intellect since that doesn't effect those talents. May cast or card pets none of the stats effect those talents.
Check the hatching kiosk for pets. Use the search function in the right hand corner to find pets with the abilities you want. There are some really good pets there.
Farm mobs for couch potatoes in Grizzlehiem. It may take awhile to get some plots going but once you have them established it's a constant source of good mega snacks.
I forgot I had a sub to this so am only a bit into the second world. The bear world you mentioned is like level 30 I think. My current pet has a resist on it, says 8% across the board, a talent that raises her stats and one the blocks 3%. I haven't trained her much further because I have 50 some energy and it takes 8 or 10 per game now.