This is what i'd do:
Buy brake cleaner and (optional) brake lube and copper paste.
Discs
- clean the discs with brake cleaner.
- gently sand the discs (hand or drill) to get most of the rust off, the rest will be removed by braking. Use fine sandpaper to avoid scracthing the discs too much.
- if you have access to compressed air, use some to blow off the loose rust. Then clean them again thoroughly with brake cleaner.
Caliper & pads
- spray the caliper properly with brake cleaner and clean with a rag
- remove the sliding pins, sand them very gently if they're rusty, and apply a thin coat of brake lube
- remove the pads and retaining clips. Sand gently the retaining clips if they're rusty.
- Put the clips back and make sure the brakes can move in the caliper. If the fit is too tight, first make sure the clips sit properly in the caliper. If the pads still feel tight, you can sand or file a bit off the top and bottom where they meet the clips. Once the fit is good, apply a bit of copper paste to the top and bottom where you just sanded.
- Push the piston back, apply some copper paste to areas that will touch the pad and re-install the pad.
I'm pretty sure this will cure your problem. Brake jobs are pretty easy once you've had a go at it. But i'd probably still start with just cleaning and sanding the discs, then go for a test drive and do some hard braking. If the grinding and squeaking continue (and/or you want to do this properly), then service the calipers and pads.
Hope that helps!