It really depends on what's going on in the scene.
Melee - there are different techniques that can be used with the camera to fool the audience into thinking that someone got punched or kicked. For example, when we need to punch somebody in our films, we punch past the person. Like you want to punch the air on the side of their face (and follow through with it a little bit) and the other actor must turn their head in that direction. It looks very real. This goes for crosses, hooks, uppercuts, and other punches. Hit the air around the face and get the right camera angle and it'll all go well but it takes a little practice.
Guns - very broad use of different angles. Close ups, trucking shots, wide shots, anything. The audience needs to know what's going on. Unless you want the audience to feel what the character is feeling, like confusion, which would get the audience confused to but that's a double edged sword. Usually, when we film action scenes, we make the camera move a little bit. I can't think of the term right now, but it's pretty much just holding the camera in your hands and moving it a bit around on the shot to give it a bit of a frantic look. Multiple shots, remember that.
This is just what I've learned from experience.