I use Mother’s aluminum polish. It’s amazing
I second Mother's Mag, but with a couple of caveats:
1: For a good mirror shine, you need to prep your piece in advance. Wetsand it through the grits to 800 miniumum.
2: Wear gloves when you apply the stuff. it's not that it's toxic, but any skin oils on your hands will mix with the polish and dull it.
3: If you plan on handling a polished piece regularly, you'll need to repolish it every now and then.
4: It's a lovely shine, but you can't put any kind of clear coat over it.
5: Don't get the stuff in screw threads.
6: A jar of Mother's Mag only has a shelf life of about three years. once it starts decomposing into a yellowish oil and a beige cream, bin it.
Side note, Mother's Mag also works great on brass and copper, but with all the same caveats.