You’ll need things produced by many of these professions to optimize your character, but you only get two professions you can do yourself. Unless you want to grind on a second character to collect all the reputation-gated recipes for other professions, you will probably need to buy the stuff you can’t make for yourself on the auction house. And if the price of the stuff you need exceeds whatever your questing and your followers are bringing in, you might want to sell some of your own trade goods or raw materials in order to finance your purchases.
Blizzard changed the leveling experience at the same time those new characters became available. It used the scaling tech available in its later zones to make broad swaths of older areas available to a much wider level range, so that characters could choose what quests or zones they wanted to do and stay there, rather than out-leveling them too quickly.
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