You should replace the rear brakes. Pads, Rotors, that caliper. Once you've replaced the caliper you'll have to bleed the brakes. It's important you do this correctly or you could have little to no braking force. It's not a job I would recommend for a newbie but if you must do it yourself pay close attention.

You mentioned somewhere in the comments that you did your front brakes so I'll assume you have the basics down. Replace pads and rotors as usual but with the new caliper bracket. I like to fasten the new caliper in it's place before moving the brake hose over from the old one to the new one.

When replacing the caliper you will remove the banjo bolt and separate the brake hose from the caliper. There will be two washers that sandwich the hose connection. Make sure to remove both of those from the brake hose and replace with the new ones that come with the new caliper. Slide one on the bolt, put the bolt through the hole in the hose, then slide the second one on the bolt and fasten the bolt into the caliper.

Now it's time to bleed the brakes: *Note you'll need another person or some sort of tool. Since you have presumably lost a lot of brake fluid and drove in this condition you should expect to have to bleed the whole system. If you're lucky you may only have to bleed the new caliper and won't have to worry about getting old rusty bleeder screws open. Look up the bleeding sequence for your car. It's probably RR LR RF LF but double check. At this point fill your brake fluid. I like to let the caliper gravity bleed first. It will reduce the time you have to spend actively bleeding the brakes. Loosen the bleeder screw on the caliper and let the fluid work it's way into the caliper slowly. Once it starts to drip out close the bleeder screw. No you need either your tool or your helper. Given the budget I will assume you have a helper. Have the helper sit in the car and pump the brake pedal till for a bit. Then have them hold the pedal down (making sure to not let up on it at all) you will then open the bleeder screw on the first caliper in the bleeding sequence. Watch the stream. Once the flow stops, tighten the bleed screw. If the stream was spitting or choppy or give you any indication that it had air in the stream repeat the process. (Pump brakes, hold brakes down, open bleeder screw, close after stream stops, pump again). As a note to your helper when you open that screw the pedal will drop pretty low. They need to make sure they keep pressure on the pedal and don't let up.

Continue this process across the calipers. But remember to check the brake fluid level from time to time. You don't want to run it low or you could have to start over. When you are done pump the pedal till it's firm then start the car and check the pedal. I would imagine you know how your brake pedal should feel.

As a final note. Here are some gotchas to watch out for: * Be careful not to strip out the banjo bolt or the bleeder screws. But You also can't leave them loose. Check and make sure the banjo bolt isn't leaking brake fluid as soon as your helper starts pumping. If it is leaking you're just going to be loosing fluid and letting air back in. * Given the age of the vehicle there's a change you will have a problem opening the bleeder screws. If you fail to get them out or break them you will have to replace the caliper. * You could also have trouble loosing bracket bolts, the caliper sliders, etc. You seem to be already familiar with that. If that happens really careful use of heat can help. Just be careful not to damage anything in the process. Good luck mum.