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.
The Hearthstone has a cooldown of 30 minutes, but there’s a guild perk called Hasty Hearth that shaves the time by half, giving you a strong incentive to join a guild. Yes, even if it’s some random guild that invites you without warning. It may feel odd to join people you don’t know, but if they have Hasty Hearth (and most guilds do), joining can save you a lot of legwork.
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.