That is a difficult question to answer in one post. I'll try to break down specific questions:
My budget is fairly limited, ideally something less than $1000
For under a $1K you are better off going for a hardtail (no rear suspension). Even though full suspension is way more fun to ride down, it makes the bike much heavier and harder to climb. Having a rear shock dramatically increases the cost of the bike for manufacturers and that cost is passed down to the customers. So hardtail mountain bike would be my recommendation.
What wheel size? It seems like the main tire sizes are 27.5, and 29er. It seems like fat bikes are becoming popular but I think that might be a little too specific for me.
For the wheels size I would marginally recommend the 27.5. But if there is a better deal for the 29er, I would pick that for sure. The wheelsize difference isn't that important for the entry mountain bike. Don't bother with fat bikes unless you have very specific riding conditions such as snow or mud where those bikes really stand out.
What style? It seems like the main differentiator is hard tail vs. full suspension in this space. It seems like this is further broken down into Cross-country, enduro, downhill, trail etc. etc. Is there a particular style that would be better for a roadie to transition with? I feel like a hardtail might lead me to riding trails that would be a little more endurance oriented than skill oriented, but I'm also a bit worried that I might be limiting myself, and giving myself a less forgiving ride.
As I've stated above going with a hardtail due to budget constraints is your best option. Riding a hardtail will also improve you mountain bike skills so when you finally have enough cash to affort a full suspension bike, you'll be ripping it down the mountain with confidence.
Hardtail also helps with building up endurance and unlocking trails that aren't worth riding up on a full suspension bike. My guess is that if you start enjoying mountain biking, you'll end up having 2 bikes anyway: a hardtail for climbing and a full suspension for descending.
I'd recommend looking into Diamondback as they sell directly to consumer thus passing the savings to you.
Sometimes you can find a good deal at a local bike shop or hunt for a used bike on Craigslist or Ebay. You'll be surprised to find just how much you can save on a bike that someone bought new and kept in a garage for a year only to realize that they don't need it and will sell it for 1/2 off. That is always the best deal!
TLDR, hardtail under $1K budget with a steep discount (like 40% off or more).