Sennheiser HD599 and a modmic. Open back, mostly neutral with Sennheiser's slightly mid forward 'house sound'. Great for almost any genre but excelles with rock and pop and vocals in general. Doesn't need a headphone amp.
Beyerdynamic DT770 32 ohm and a modmic. Closed back with a V shaped EQ. Meaning the highs and lows are boosted. Closed back so they don't leak sound and you won't hear what's going on around you. More EDM and hip-hop specialists but also more 'exciting' for gaming. Some find the treble to be very bright on Beyerdynamic headphones. No amp needed. The 80 ohm version probably sounds better but you'd need at least good onboard audio from your motherboard to drive them.