The top of a bay window I have is covered with a metal sheet. The patina and color of the corrosion on it suggests that it might be painted copper.
What sort of paint should I use to freshen up this sheet?
Since you are asking about painting the copper:
The key to a successful painting is getting the paint to stick. The right paint does nothing if it fails to adhere.
By "succesful painting" I mean a job you won't have to re-do every couple of years.
You do all the usual light scraping to get the loose stuff off. But for the final prep pass, go at it with Scotchbrite pads. Obligatory huge product shot here.
You're not trying to polish it, however you are trying to assure everything gets covered with microscopic scratches, and anything thick enough to present an adhesion/separation problem is gone.
Of course, if you accidentally did polish it, you could coat it with an oil-based varnish to keep it from oxidizing.
After sweeping away any particles/dust, oil is your remaining enemy. Your final step of prep is to wipedown in solvent (whatever the paint solvent is, typically paint thinner). If it's water based (I'm not a fan of water-based for challenging jobs), then wash it with soap and water, thoroughly rinsed.
Then follow with your primer of choice, then topcoat. I'll never be a fan of "primer and topcoat in one can" products. There's only one paint formulation that does that well, a 2-part epoxy such as Amercote (don't bother, it's not for consumers), and epoxy is allergic to sunlight so it needs a topcoat to stop it from quickly failing. Generally primers don't give you a choice of color.
If your ultimate destination is a dark color, Rustoleum 7769 Rusty Metal Primer is actually made to prime metal, and is readily available.