My friend with that budget your options are pretty open, but being on this website you should know full well that there's no such thing as best. So for others who've listened to a much broader range than me can also input options what are you looking for?
I.e.
In terms of sound do you like your music more warmer, brighter or perhaps complete reference (unbiased in its sound)?
As far as fit, do you prefer an in, on or over ear option?
lastly would you want the ability to listen to these portably or will they only be used at home?
For
ME personally the best headphones I've ever heard that left me awe struck in whatever I was listening to was the
Oppo PM-1 ($1099). I enjoy my music slightly warmer as to be nice and relaxing, perhaps not the most sonically accurate but gives me a nice sense of ease when listening providing a very sensual experience when you're just wanting to relax; but the neutrality of these was wondrously pleasant. These also sounded wonderful just from my phone but a good amp. could probably increase the sound even more (I've only a Project Horizon 3 so my recommendations are limited in that subject).
As far as I.E.M. the best I've heard is by far the
Shure SE846 ($999) these have interchangeable filters for you to really customize the sound to whatever it is you like plus they're super comfortable and don't need an amp what so ever.
I'm currently listening to the
Sennheiser HD700 ($749 but on sale currently for $519 via moon-audio.com) w/ Moon-Audio's Black Dragon Cable ($255). Honeslty for me these are alright but are somewhat bright with a notably recessed lower mid/upper bass line. Not that it's bad but for its price point not something I look for but the BD cable really warms it up a nice bit). The soundstage however is super vast and the comfort is awesome with really good detail whoring. These like the HD650 are complemented with good tube amp and can somewhat, kinda sorta be driven from a mobile unit but though you'll get ok volume you can just tell there's so much more potential available.