What you need seems to be a Non Linear Editing System (NLES), which will allow you to place your portions of video (scenes) in a timeline in order to arrange them in the position they should be so that you can "view" a one single video scene playing.
In addition, you can manipulate your video by adding improvements like color correction, gamma, brightness and contrast adjustment and other useful things.
If you wish you can also slice your scenes and remove portions of each video clip and finally do a render of your video production into a single file.
Ubuntu is plenty of useful tools for even real time video processing but if you are used to Windows/Mac Software you will feel comfortable with KDENlive (https://kdenlive.org/) and Openshot (http://openshot.org/).
My favorite is kdenlive so I am going to place this screenshots over here in order to illustrate the timeline video placement:
In this timeline I am using 2 Video sources and 1 picture. 1 of the videos is having the "Curves" plugin and I am adjusting brightness level with that plugin. As you can see, kdenlive provides several tools for audio/video levels monitoring so that you can achieve professional results from your production.
I used to work for TV/Radio Stations the last 20 years so let's say I worked with many digital audio/video file formats as from 1999. The Sony MTS is, if I don't mistake, a MP4 container unless you changed that from the options of your camcorder (if the camcorder features such function, of course) so you can mux/transcode the video files into a different file format without losing quality.
When it is about muxing/remuxing/transcoding the very best GUI Tool for ffmpeg/avconv/mencoder seems to be the Mobile Media Converter by Miksoft (https://www.miksoft.net/mobileMediaConverter.php) of which I am going to illustrate as follows:
MMC will also allow you to rip from DVD and Download from YouTube.
So. If you're involved in professional video editing you may agree that manipulating huge video files it a hard work. Unfortunately there's no "automatic" procedures if you wish to get stunning results.
But you're on your way.