I have heard that diet coke removes rust.  You'll need plenty of fine steel wool for the chrome pieces.  You'll have to do ALOT of sanding, I'm afraid.  Some parts you can either use a Dremel grinder with a wire brush bit, or even a full drill with a wire brush bit as well.  It's going to take you awhile to get all that rust cleaned off.  You can try to see if you can find something called "Rust Cure."  It won't look pretty, but in the places you're going to paint, it will help the rusted areas convert into a kind of subprimer.  Once you get everything sanded, wire brushed, and steel wooled, use a several coats of primer.  Wait a few days for that to dry.  Then, with some gloss black or whatever color you choose, do several coats of that as well.  You also have the option of using a clearcoat.  I've painted several typewriters myself--some have turned out better than others, but all in all, I did okay (I think).