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.
Anyway, there are no more shortcuts. There are no more "Tricks". It's just straight questing now since Blizzard nerfed other methods of leveling. You can still do dungeon spam, it just won't be as fast. You can still do BGs, it just won't be as fast. Just about the only alternative way to level that rivals questing is Pet Battles(which makes ZERO sense).
Our old friend Quest Helper isn’t updated for the client, but there’s !Questie and MonkeyQuest to help you track available quests and their objectives. The biggest challenge to leveling up in the beta is searching for where the quest objectives are, so if you’re looking to hit the level 30 cap fast — or just the level 5 cap in today’s stress test — you’ll need one of these.
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.