My budget is around $1000 for headphones and the amp.
Most would recommend Grado's tbh.
I would recommend Alessandro since the Grado's highs fatigue me but if you enjoy sparkly highs than definitely Grado.
For under $1000 you could easily get a used Beyerdynamic T1 though
If you're buying new, get the HE-500 and spend the remaining $300 or so for decent quality amp that will power them. The Schiit Asgard or many quality Chinese mad solid state amps, just to some of the options, will do the trick.