AviDemux works well for doing multiple cuts. It does not do any conversion of the video format therefore it saves your project very quickly. VideoRedo does much the same but it can convert video formats. It's a good choice for processing video from broadcast TV. TV stations broadcast Mpeg2 and left in this format will create very large files. The downside is that it takes a long time to convert the video. If using AviDemux, once your video is edited, you can use a free video conversion program called Handbrake. Since the OP is starting out with Mpeg4, no conversion is needed.
A trial version of VideoRedo is available here:
https://www.videoredo.com/en/Download.htmHandbrake download:
https://handbrake.fr/