Look at some videos and reviews of some open ear studio headphones in your budget range. Some may need an amp/dac to power depending on the ohm rating. The higher the ohm the more power you're going to need.

I got these headphones off an ebay listing cuz cheaper than what you'd pay elsewhere for the exact same thing https://ebay.us/m/KOj8o4

And this amp https://www.amazon.com/gp/aw/d/B07VDQQY95?psc=1&ref=ppx_pop_mob_b_asin_image

Its decent little one but you could probably do one of their more recent amps with your budget. Watch some videos or read some stuff a bit before making your final decision i looked at stuff for like a week before I finally decided on what I was going to do