FYI: If you’re returning to WoW after an extended absence prior to patch 5.0.1, it’s possible that you’ll have more than the maximum pet limit and/or more than 3 of a kind. However, this will be the only time that you’re allowed to surpass these limits. You will have to pare down your collection, eliminating your duplicates, in order to add new pets.
Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide.
The same goes for the level 40 mount. An elite ground mount means still-faster leveling. Not only that, but you'll get knocked off considerably less often by mobs while getting around inside zones, meaning you'll die less often as well. Remember, as the goblins are so fond of saying, "Time is money, friend!" So it behooves you to get an elite ground mount as rapidly as possible.