What's the best before editing format to convert to?
I would recommend downloading the trial version of Adobe Premiere Pro, and cutting the videos together in there. The trial lasts 30 days which should be enough to get the job done..

Premiere Pro can take almost any file you throw at it (so you can leave all your videos in their original format). This way you wont be loosing any quality by converting your videos to one uniform codec before you edit. 

Otherwise as a completely free solution Id suggest converting all your videos to 1920x1080p h.264 files. Then you can bring them into iMovie or Windows Movie Maker to order and export one final file. 

If you dont need the all the videos combined into one file (ie. if your player can play all the files on its drive continuously) then all you need to do is convert them to 1920x1080 h.264 files and load them on the drive.