When I started with pet battles during the long, long drought of Siege of Orgrimmar, I too found myself delighted with revisiting all the beloved old zones with a purpose.
It is really pleasant to tour the world collecting, and learning the mechanics of pet battling.
Like everything in WoW, it has been analysed to death, and I suggest you just work through the learning and beginning and collecting stages naturally rather than study the theorycrafting. They are the best, most enjoyable part!
Do please get these three addons:
Rematch
Pet Tracker
Battle Pet Breed ID
all three are essenftially mandatory for anyone collecting or battling. There are others that are optional, but those three are your basis.
PvP is not good. Long and sad story. Basically, the devs don’t want to promote competitive pet PvP, and they give it very little. The best reward is a level 25 Purple boost stone from Pet Week, and that is much harder to get than just paying 60 Charms for one at the vendor. There is no PvP apart from level 25s, and the current meta is sooo crazy unbalanced that most of the few people who did PvP have stopped.
You will need a beginning roster of Level 25 pets to do the dungeons. The Celestial Tournament, the original, is AMAZING. The others … opinions vary. Your main reward from the dungeons is more pets that you can buy with currency you earn in them.
There is also the WarcraftPets Discord where you will find lots of jaded but friendly old hands https://discord.gg/967Vu7G
I recently wrote some guides for another player at about your stage who wanted to get one of the Celestial Tournament pets. They might help you, too, and answer some of your questions.
If you want to know ANYTHING more, do check out the Pet Battles forum or the Discord!