The mutant I've been playing most recently is PopPop who looks a bit like a white triangle that seems to have a double-shot special ability (right-click).
The shotgun (a gun which fires multiple projectiles that bounce off walls) is probably my favourite, offering a run and gun process.
However the machinegun, laser pistol and assault rifle all offer a different game experience of hanging back and focussing more on accurate shooting. The laser pistol and the machinegun don't kind do enough damage for my liking, making the assault rifle more appealing.
The mutation I really like is Scary Face, which reduces enemy HP.