I'm happy to see them really committing to this. I didn't think I would be all that interested, but I will sure give it a go. Personally I wouldn't mind quality of life improvements and most of my friend don't really care for a 100% authentic vanilla experience but they want the old zones and world, a game world pre-Cataclysm but have no requirement for it being "authentic" to World of Warcraft Patch 1.12.2.
To actually get access to the beta, which has already started and continue to add more players, you need to sign up via your Blizzard account management page. Under Games & Subscriptions, scroll down to Beta Access and visit the Beta Profile Settings page. Once there, you’ll see a grid of available betas you can opt into. Once you’ve checked WoW Classic, hit Update Preferences and you’re set.
Apparently a lot of the current World of Warcraft Classic closed beta testers are reporting things as bug that, well, simply aren't. There are enough of them, in fact, that Kalvax, the Classic community manager, posted a lengthy "Not a Bug" list on the forums. Some of the things that are actual features in the game include Tauren melee reach and hitboxes are larger than other races, Warrior health regen is working as intended and creature respawn rates are "much slower".