You should equip new quest rewards when their item level starts beating out your previous set of gear. If you are currently wearing Tier 21 gear, it is best to let the quest rewards significantly beat your existing item level before using them. With that said, you will unlock Azerite pieces early on, which are worth using over Tier gear in most circumstances.
Most classes in World of Warcraft start at first level, but Death Knights and Demon Hunters are exceptions. They start at level 55 and 98, respectively. This alone can shave a huge chunk of time from your leveling experience. Of course, it only works if you want to play a Death Knight or Demon Hunter, but they’re both solid classics that can dish out damage or tank in a group.
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