What types of combat do fans of Heroes enjoy?

Hand-to-hand combat, because out of everything mentioned, it's a unique form of martial arts. A "hand-to-hand combat specialist" will defeat a karate practitioner, a boxer, etc. (well, assuming they have the same level of experience). Although, regarding Eastern martial arts – I don't know.
P.S. Hand-to-hand combat is taught in Special Forces.

But in general, it's better to resolve everything without fighting, because you can't fight against a gun.

As they say, "there's no solution against a crowbar."