your slide pins may be hanging up or your caliper is also hanging. When you take the right front wheel off, check the slide pins on the brake where the caliper is mounted to it. They should slide in and out freely. If they don't, don't even bother cleaning the rust out of them, just heat them up and twist the slide pins out of the bore and clean the bore of all old grease and then buy a new slide pin and grease at the store.
If the slide pins are sliding in and out without any hanging, check that the brake pads are sliding on the anti-rattle clips freely. If it is bound up, try to take a stainless steel brush to the rattle clips to clean them up and then put some brake grease on the rattle clips where the ears of the brake pads mount into.
Before you bolt it up, take a bar that is big enough to go over both pistons of the caliper and use a c-clamp to depress them. If it has a lot of resistance or one moves easy and the other is hard, you have a failing caliper and you could get it rebuilt but I myself just replace the whole caliper.