This option is better to use at level 40+. Higher level you are is better, more money you make then. All you do is farming dungeons or specific bosses. Here you kill a few birds with one stone: you get lots of experience (make sure you have all quests in your quest log, always ask your teammates to share) if you are still leveling; improve your current gear; and loads of loot (clothes, recipes, even crappy grey items selling for a lot to a vendor). If you are in a group, think about your groupmates if they need an item or not, don’t roll need on everything.
However, after a while the novelty of it wears off and you do start getting a little bored of all the eating and drinking (and wondering why your character isn't getting to Kul Tiran levels of fat), especially if you hop on to BfA for a bit in between. The difference is huge and once you're used to just slamming into 5 mobs and downing them quickly it can get a bit boring to just pull 1 mob at a time and then wait and wait. The really low levels aren't that different between live and Classic in terms of gameplay however, as the small amount of abilities means combat isn't exactly the most exciting thing in either. On live you get past that pretty quickly, but it takes a while longer in Classic (especially if you're playing solo).
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.
FYI: If you’re returning to WoW after an extended absence prior to patch 5.0.1, it’s possible that you’ll have more than the maximum pet limit and/or more than 3 of a kind. However, this will be the only time that you’re allowed to surpass these limits. You will have to pare down your collection, eliminating your duplicates, in order to add new pets.
In the end, while it may be a huge cop-out, it really does come down to personal preference. Some people will simply not be able to handle the huge downtime between pulls, not being able to buy a new skill rank because you spent all your money on food and drinks (mages were popular for a reason back then), the very slow pace of leveling, and a whole lot more frustrations and not user-friendly features. On the other hand, the experience really is significantly different enough from modern WoW that it does feel enough like a "new" game, or at least a new and different expansion. An expansion that has many more differences than the last 3 or so, something that's both new and old and familiar. And, yes, it also offers massive quantities of nostalgia for those of us that played Vanilla, but what's so wrong about that?
Only really to expand on Gráinne's comment as regards the 'collecting' and 'roster development' sections - which are, as said 'distinct' although they are intrinsically linked - I would like to point you in the direction of the in-game Achievements > Battle Pets > Collect tab. There are a series of achievements called Raiding With Leashes, pretty much all of which can be completed via the auction house - if you have the gold/inclination - or by completing old raids.