What is the simplest way to cut and put together many parts (for which I know the timestamps) of many videos? I am absolutely new to video production, I just have a simple job to get done.

I have about 10 videos of a few minutes each. I want to take the interesting parts of each video (there's maybe 3-6 interesting parts per video), put them together into one video, and discard the rest. I have sat through each video and recorded the timestamps of the beginning and end of each part in each video I want to keep. E.g. Video 1: 00:36 - 00:39, 01:04-01:20, Video 2: 01:36-01:39, 02:24-03:00, etc. 

Is there any program that would allow me the simplicity of typing in the timestamps of each part of each video I want, and then put it all together as one video? 

Additionally (although this isn't currently a necessity) it would be nice if I could put in a title (I'm thinking white text on black screen) before each part of the final video to explain what will be shown next. Or at least have a caption on each part of the video.
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.