If you are willing to buy used, I would highly recommend the Fostex TR-X00 line (about $400), preferably the ebony (refined V shape) or purple heart (bassy fun V shape). These are both great headphones with biodynamic drivers which are known for great bass, but the TR-X00 line can be a bit to sharp for some (I find the purple hearts are almost never to sharp, and they have the most treble of the three variants). If you think the treble might be an issue, then the audioquest nighthawks (about $250) might be up your alley. I have no personal experience with the nighthawks but there are plenty of others on this forum who do. From what I hear they seem to be a dark but still detailed warm headphone with great biodynamic bass.
To be clear, both of these can only be found used, but you should be able to recoup most of, if not all of what you paid if you end up not liking them.
Neither strictly NEED an amp but something like a schiit asgard 3 ($200) for an amp and a schiit modius ($200) or a Topping e30 ($130) for a dac will be more than enough for most sub $1000 headphones.
If you want a truly open headphone (as both that I have recommended are only semi-open) and/or want to buy new, then the drop x focal elex ($700) are a good choice. Again, I have no personal experience with them but many people hear do. Also if you thunk you’d like the TR-X00 line but want to buy new, the TH-610 ($600) are a good option that are a bit more neutral than the TR-X00 line but still a good V shape with high quality bass.
Here are links to the relevant discussions