Elixirs serve the same purpose as Flasks, but the buff expires if you die. You'll only use these between 1-70, generally speaking, until you can start buying Flasks which persist through death. Try not to die, and carry extras just in case. If you can't find an Elixir with the stat you want, look under scrolls, since they count as battle or guardian buffs as well.
First, a bit of context: I've been playing the game since six months before it was originally released, and I make no apologies about liking it. It's getting long in the tooth, as with all games that have been on the market for 14 years, but Blizzard seems committed to continuous improvement. The last expansion, Legion, was the best the company had ever released. (Stop arguing, Wrath of the Lich King fan boys. It's true and you know it.)
In addition, you'll want to pick up leg and shoulder enchants and have them in your bags. These enchants have a level requirement of 80/85, but can't be placed on items above iLVL 136. You can get around this by having a level 85-100 character apply the enchant before mailing it to the character you're leveling, thus getting use of the enchants before level 85. I've personally confirmed that this works.
If you love running old content for transmog items, you'll love the new legacy loot system. Whenever a player enters a dungeon or raid where they are 10 or more levels above the content, the dungeon or raid bosses drop an amount of loot equivalent to what would have dropped for a full group when the content was current. That means players could earn loot for five people in dungeons and loot for 20 people after soloing a raid. The legacy loot system also drops other gear types, like cloth dropping for a plate wearer. It's now much easier to get the transmog gear you want, and you can also collect gear for your alts on the same run.
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.
-New dungeons- About 3/4 are fairly decent, not too long not too short, but none of them are compelling, none make me say to my friends and guildies, "Hey, let's do this instance, I love the theme and encounters." They're dull but tolerable. The other 1/4 of the dungeons just aren't fun and you will groan when you get a mythic Keystone for the Underrot, the snake temple, or Waycrest Manor. Waycrest Manor is actually one of the better dungeons, however, with the new Infested affix, Waycrest Manor suffers from many game-breaking bugs that end in the entire instance being pulled due to doors not properly working as intended.
I do not recommend going for TBC, although I remember Hellfire peninsula to be decent, everything else is rather slow. Instead go for WotLK, Borean Thundra gets you levelled very fast, and then you can head straight for Icecrown at 67, which is also insanely fast, although admittedly has a few elite quests. You can go to Sholazar Basin alternatively. 2 zones should get you 60-80 no problem.