There are four phases of restoring old brass:
1. First you need to clean off any grease, oil, lacquer or other contaminents/coatings on the surface of the brass. You need lacquer thinner, paint stripper or acetone to do this efficiently. If you try to do this with simichrome or brasso on previously coating brass you'll be polishing for a very, very long time.
2. Once your brass has nothing on it's surface you can remove the oxidation/tarnish/metal discoloration/etc. Phosphoric acid, Nitric acid, vineger/salt or lemon juice will do this much more effectively then metal polish. (toilet cleaner's often have phosphoric acid as the active ingredient)
3. Once you're down to a dull/consistent brass finish you can polish away to gradually bring up the luster. This is the phase where you use brasso/simichrome/etc. However a buffer works so much better along with cutting/polishing compounds. (Tripoli then red rouge works well).
4. Now you better think about protecting the finish or it'll revert back to where you started. Clear nitrocellulose lacquer like Nikkolas Clear coat works best on brass.
I collect fans and have spent tons of time restoring old brass.