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.
Like with addons in the current game, you just need to drop any of these addons into the addons folder — find it under /Interface/AddOns/ in the Classic beta folder, which is in your World of Warcraft folder by default. Then once you log on to the game, you’ll want to make sure that the addons are enabled via the menu option on the character screen.
Drustvar is far and away the hardest Alliance zone, which is exactly why you want to do it first. If you have legendary items, they’ll still be usable, and if you don’t, this zone will still be easier early on than it will be later. Drustvar is also extremely fast and will let you jump out ahead of your competition in other zones, which means fewer players around to take your quest objectives.