Those spots are not bad, you really don't need to worry unless you are just picky.
Are you doing a bolt-mod? If you are cutting the plate free you have the ability to do more harsh and complicated procedures on it.
If you just want to touch it up, I would use steel wool or light sandpaper to remove the rust.
"Naval Jelly" (not to be confused with navel jelly) is a great product if you really want to fix it good. It is a pink goop (made for ship repairs - surprise!) that neutralizes rust. Probably costs $10 for a small jar.
If you don't want to take the time and trouble, paint some Rust-o-leum paint on it (the oil-based type includes a rust killer) or just rub it with machine or gun oil that specifies "prevent rust" with a rag. Fingernail polish is probably OK, whenever the wife gets tired of a color I keep the leftover on the workbench for this sort of thing. That will probably hold it for quite a while as long as it stays dry inside the case.
If you are doing the bolt-mod, clean and buff the whole plate, and then paint, varnish, or oil-rub it to your heart's content. Try not to leave any excess.
There are many coatings and polishes for metal, but nobody ever sees that plate, except you, so spend your time elsewhere.
The early ones had a glossy finish that was different and prettier. Heavier plate, too.
