What sounds like more fun to you - fast, open, twisty, relatively smooth trails or jumping log piles, ripping through streams, and dropping a few feet off rocks?
If the former, go hard tail. The latter, go full-suspension (all-mountain).
You can absolutely do either run on both bikes, but each have their pros and cons.
Also - and I can’t understate this - do not buy new (yet). You can easily buy an incredible used bike for $600-1000 that was $2K+ new. But here’s the kicker: if you don’t like it you can easily sell it for what you paid, sometimes more. It’s almost zero-risk.
I personally can’t stand the ride feel of a 29” wheel. Yes they roll over stuff more easily, but turning quickly or sharply sucks. Just feels cumbersome after riding the classic 26” for 20 years. (Another reason to buy used.)
While that Specialized is surely better than a Walmart bike, it’s really all about the components.
You should honestly be fine with anything at the SLX level or higher (XT is next, XTR is out of your price range). Whatever SRAM’s middle of the road is fine too.
If you really want to support your LBS check and see if they have used and allow trial periods. Otherwise, Craigslist. Or for the best selection www.pinkbike.com. Ignore the misleading name as it’s an incredible MTB community with tons of bikes and parts for sale. I got my oddball Trek 69er in like-new condition for $900 (retail was $2400) from there.
Whatever you end up doing, I’m sure you’ll have plenty of fun.