There is just so much to choose from - if you have a dealer in your area where you can give a listen, try to do so; it might make it easier to decide if you want to go planar or dynamic, or either.
There are wonderful tube HP amps out there as well, many designed and built by one person (in my case, I have an Eddie Current Studio B and a Donald North Audio Stratus). I'd guess classical music would sound awesome on them. And even though they are relatively low powered, I can still drive my Hifiman Susvara's quite nicely without having to crank it up to max volume. Focal Utopias sound great through them, and you can find them used in your price range.
But I'd suggest you buy from someplace that will let you return the headphones and/or the amps if they are not to your liking after burn-in time, and many headphones and amps (and tubes) need a LOT of burn-in time.