Doesn't even have to do with new pets, but as you look for those new pets and try to get your pet battles in, be on the lookout of older pets that would be upgrades for your collection.
This maybe doesn't even mean rarity upgrades, although if you need some those are certainly still possible. However, I was referring more to instant level upgrades you can find as secondaries as you battle.
I have found a multitude of secondaries that you just wouldn't expect, and in many cases you can get level upgrades if nothing else. In just a short time, I have seen skunk, rat, squirrel, various snails, red-tail chipmunk, various moths, and so on, that have been unexpected secondaries. Even though I have a very robust collection, I have already gotten two 'freebie' upgrades for skunk and red tailed chipmunk that I had lower level 6s and gotten poof 23s just by capturing on a secondary.
I know, a very elementary tip, but everything helps, right?