The next thing to do with this saber is to get it cleaned up and protected from further corrosion... Whatever you do, don't use any kind of abrasive on it, I would give all of the metal a good dose of gun oil and let it soak in a bit before gently wiping it down with a soft sponge. Don't try to do too much at a time, add more oil, clean the sponge or change it out often as needed and wipe it clean with a soft cloth often to see how it's cleaning up. Also don't go too far with the cleaning, if you think you've gone far enough, you probably have. Do the same for the scabbard as well and use a good amount of oil to flush out any loose rust if possible.
If you're not comfortable doing all of that yourself there are people who can do the work professionally
Once cleaned, I would keep it out of the scabbard for display and storage since there will be a good chance that it could rust again. be sure to oil it up and wipe it clean every so often to preserve it