What is the simplest way to cut and put together many parts (for which I know the timestamps) of many videos?
Cutting and arranging video material is the most basic thing that any video editing software has to be able to do. You won't find any NLE that can't do that. Titles are pretty basic as well, you can insert titles with software as simple as Windows Movie Maker (though of course more sophisticated software will always give you more control). So yeah, as Michael Liebman said, pick one.