Drum brakes grinding noise at start of each drive

My 10" front drum brakes make a scraping/grinding sound every time I start driving. After a few stops they are quiet. I'm about to switch to disk brakes anyway, but I'm just curious what could be causing this. I don't think it's rust because it happens even if I only stop for a half hour. I'm guessing it happens only when the brakes are cold, but why?

More info: the drums and shoes are old, but the car stops pretty normally except every once in a while it pulls to one side on hard braking. There's also a loud medium-pitched hum when I stop in reverse, but that's all the time even if I've been driving. Also, I've just completely replaced the rear brakes with no effect on the noise.