If you've added any skins you want to keep, or any other customisations saved in the "Data" directory, make a backup of "C:\Program Files\J River\Media Center 16\Skins" and also "C:\Program Files\J River\Media Center 16\Data"
Once you're up and running again, if you restore your library from one of your automatic backups (which you should have in your application data backup), you have the option to also restore your MC settings too. If your music files have the same path on your new computer as they do on the old one, you'll be good to go from there without missing a beat. If the paths have changed, you can use the "Find / Replace" part of the "rename, move and copy" tool to update the paths in your library to match the location of your audio files, and then you'll be good to go.
Good luck, and if you need any help on the other side, just ask.
-marko