I would replace the caliper. It’s probably abt 15 bucks or so. And there are two bolts, generally that hold it on and the brake line – thats it. Just remember to use a flare nut wrench (Invest in a set if you don’t have one) to break the brake line loose – learned that lesson the hard way once or twice – if you round over the break line nut, uh its easier to just do it right the first time.
Once in a while, I’ve seen where if the piston moves in or out on one side too far it will release a little fluid. However it generally means the seals are bad in there…you can also buy a rebuild kit, but I’d just buy a whole new one, they aren’t much different in price / dollars.
For brake bleeding, you dont need anything fancy…don’t get talked into buying the mityvac kit (garbage, imo), you can make your own for penny’s or just buy the dirt cheap otc junk one for 7 bucks…You’ll need someone to press the brakes for you, for bleeding the line, but its really really easy to do.
Good Luck!