I found that in most cases, I could pick the zones I liked and skip everything else. It was slower, but I still wasn't forced to do quest zones I hated (and, notably, I skipped the entire Cataclysm expansion's content -- sorry, Thrall.) I did do dungeons, both in group finder and by two-boxing (more on that in a moment as well), but only once for the quests, and mostly to clear what felt like an awfully long slog from 40 to level 80.
Cooking benefits all classes, especially melee and hunters (it is a free source of food). Until higher levels, the benefits it provides are almost exclusively stamina buffs. While more stamina is always nice, cooking is not essential to leveling. Considering the time investment required, if you pick up skinning then cooking would absolutely be a wise skill to level prior to hitting your level cap, as beasts often drop meat useful for skilling up.
Professions: This may seem strange for a leveling guide, but the first opportunity you get, pick up both the Mining and Herbalism gathering professions. Not only will this allow you to track many various quest objectives on your map, but you also get a fair amount of experience whenever you gather. I'd put it at around 10% of a quest turn-in per gather. Since most of your wasted time in WoW is travel time, stopping to gather ore or herbs can keep your exp/h rolling as long as you don't go too far out of your way. You should only gather if it's convenient, and on the way to an actual quest objective. Don't make gathering your priority.
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