For semi-open headphones:
Superlux HD681, 681b, 681f, or 668b.
Alternatively, Samson SR850.

If you want a cheap Beyerdynamics DT770Pro experience, the Superlux HD660 is as close as it gets. Obviously, bass extension is no where near the DT770 but everything else is almost on par with it.

Use the remainder for a mic.

If you absolutely need a headset, the only headset I can recommend is a Steelseries Siberia V2 which is out of your budget.