Hiya Hilly,
Man! This is one of those can o' worms kinda questions. You'll find a big split in the community over whether you should even paint the drums at all. Some feel that painting will help insulate the drum so that it retains heat. Not a good thing. Others say, "Hogwash" and go ahead and paint saying that accumulated rust will insulate just as well as, if not better, than a coat of paint. Where's the truth lay? Who knows?
I'm not a guy who likes rust in any form on any part of my vehicle. So, I do paint the drums. Just a light coat to prevent rusting and it's been fine. I use just plain old rattlecan flat black and it's held up fine.