Hi there,
A few well reputed 'HPs' that can be got for under $200
- Audio Technica M50x
- Philips Fidelo X2 (just a shade over $200). You can get a lightly used one in your budget
- HiFiMan He400i. However, this may need a good amplifier since this is a planar HP
- Bayerdynamic DT880 premium
- Bayerdynamic DT900 pro
- AKG K701
You can check out head-if.com for some good reviews and pricing advice. The philips and audio technica are good options if you do not plan to get a headphone. They work well with mobiles. Bayerdynamic also has models that are mobile friendly - look for the low impedance ones (32 Ohm models)
best,
APK