Blender

Blender IS FUCKING LIT. But deep as hell.

Start blender, change the "screen block" (first dropdown to the left from the far top-left corner) to Video Editing
Now you have three areas, what I'll call top-left "graph", top-right "video preview", middle "video sequence", bottom "video playback"; each has a viewbar at the bottom of the area; in the "graph" area, select the area type dropdown (far left) and change it to "properties"; note that strangely, the properties ares has its area type dropdown at the TOP of the area, doh
In the "video sequence" area, click Add > Movie to get a file browser and pick a movie file; I like to change the view to list and sort to by date by using the toolbar
Set the End frame in the video sequence to give enough width to fit the videos, eg 250 > 25000; use the scrollwheel to zoom out, and ctrl-scrollwheel to center the sequence
Set up smaller "proxy" videos for each video strip you import; right-click video strips to select them, in the properties to the right select [x] use proxy 25%, then click rebuild; hover over the clip, press N, select Proxy render size 25%; repeat for all strips
When rendering output, use top-right properties to change output > file format > H.264, directory to (project)/output, Encoding > Presets > H264, Audio Codec > MP3

On a strip...
- press K to cut it
- press X to delete it
- press G to move it left/right/across tracks
Click in the video sequence to set the current position; press M to leave a Marker there that can be returned to using the Marker menu