UNDER $500 new.... it gets tough. At $500 (MSRP) you can get a perfectly OK bike for riding around the neighborhood and on gentle paths, but off-road capability will be limited.
If you can go up to $600, bikes like the Trek Marlin or Giant Talon are decent options, and will handle off-road fine, but don’t expect a lot.
You could probably get something decent from BD for $500, but I would only do that if you want to wrench your own bike and have the ability to check the build.
When looking at mountain bikes in the $500 to $1000 range, every little bit extra you can afford will make a very noticeable difference. Even just going from a $500 to $750 budget will make a huge difference. And $750 to $1000 will as well.
For under $500 I would be looking at used.
While the idea of rigid sounds good, I don’t think you are going to have much luck finding a decent rigid mtb new for $500. Unfortunately, the mass market demands to see a suspension fork on the front of a mountain bike, no matter how crappy it is. New rigid mtbs are more of a niche thing, thus are rarely seen in entry level price points.
And to be honest, even if you could find a new decent rigid MTB for $500, buying it with the plan of upgrading it with a suspension fork is a waste of money. You will end up spending $750 to get a bike you could have bought for $600.
OTOH, if you can find a rigid bike in your price range, I would go with that over a the crappy suspension forks that they are typically speced with, and just leave it rigid.
Of course only you know what you can really afford to spend on a bike right now, but one thing I will warn you about is that with a $500 mountain bike, if you start enjoying riding off road, you’re going to quickly outgrow it and end up buying a more expensive bike anyway. Or upgrading stuff.
The two most expensive ways to end up with a bike worth $1000 are....
1) Buy a $500 bike, and then buy a $1000 bike
2) Buy a $500 bike and then spend $1000 in upgrades.