How does one prepare antique ceiling tiles to hang?

Clean with a scrub brush and soap and water. If you are just trying to take off years of grime, Dawn or Mr. Clean or something of that ilk probably will do fine. If you are trying to degloss the paint and clean at the same time, use TSP. Follow the instructions carefully and wear gloves as you wash.

Let dry. You can help along the drying process by wiping dry or using a hair dryer or heat gun.

Sand down any imperfections or bits of rust that pop up. Wipe away the sanding leavings and prime with Rustoleum primer. This is an added layer of protection and helps the coat of paint you apply next to stick to the tile.

Sand any imperfections (of course, you won't have any) and paint with Rustoleum. Go with 2-3 light coats rather than one heavily-drenched-I'm-gonna-conquer-this-thing-NOW coat. Certainly you can add more, but 23 light coats should do the trick.

Being in a high humidity area, you can gain added protection from applying several light coats of a clear polyurethane. A belts and suspenders approach, but one that should last you a long time.

I think the 23 light coats meant 2-3 light coats.