In my admittedly limited experience: You want to start with the least abrasive thing you can use that might do the job. Oil on a rag is shockingly good at removing light rust. Disassembling the whole thing might be fun. It might be hard to put back together, but if you're up to the challenge it will let you get at all the moving parts and clean them all up like brand new.
If oil on a rag doesn't work, you could try a slightly stronger degreaser. Simple Green has been really good on a few things I've tried it on. After that, you might go to something abrasive like steel wool. But be aware of the fundamental tenet of removing scratches: To remove a scratch, you must use an abrasive that makes marks as deep and big as the scratch itself. So that might mean that you need (for example) 320 grit to remove the scratches completely. Then you'd need to step up through a progression until you got it to the level of polish (or matte) that you want.
Just some thoughts.
Brian.