you should definitely look into the video functions of blender. Though the editor is pretty simple, you have the possibility to stuff your videos into the render pipeline - along with the node compositor and your 3d scenes - which is very cool.
If you plan to do all your video work in linux, you won't be set with one software anyway. The most advanced nle for linux is cinelerra
but it has its glitches and the timeline is fiddly to use. For the not-so-advanced stuff there's also openshot, kdenlive, pitivi and several more.
If you don't mind booting to windows to get a better result, take a look at lightworks
. This is a really professional software, that has gone open source.