Windows movie maker works fine for that. It should be already installed on your computer if you have a pc and it can shorten and put together as many clips as you like. I personally use corel video studio but im really into a lot of different types of video editing. So I wouldnt suggest that unless your going to be constantly making videos that need a ton of editing tools.
If you know how to split the clip you can cut stuff out. You just split the clip in two places instead of one and delete whichever part of it you don't need :) unfortunately, theres no direct button for cutting stuff out but you can still do it that way.
It depends on which version you have. Play the clip until you reach the part you want to split. Then pause it. I believe you can right-click and thatll be one of the options but on the older versions it might just be under the little preview screen on the right side. (its a little button that shows a strand of film cut in half I think) just click it and itll automatically seperate.