I miss the cartridge days too but this is not so practical anymore. Also you'll get the best results with DRM-free games, whatever you decide.

What I would do is, buying a big HDD and fill it with installers. You can put cover images on/as folders if you want.

For save files, build a sync structure on a server (local one would be more feasible with something like syncthing). You can do that with Nextcloud or Dropbox etc. as well.