If you have room a 10 gallon is a good size for a hospital/quarantine tank. Most med are dosed in for 10 gallon increments. But if you don't have room, a smaller tank will do.
I have a 5.5 gallon tank, no substrate, a couple decorations, no light. I keep it simple since it is a temporary home and less to clean if anyone gets sick. It is also my baby growout tank, since my bristlenose catfish have been breeding like crazy. I keep mine running full time, if I have no babies, I season it with a couple drops of pure ammonia every couple days to feed the filter. Some people keep an extra sponge filter in their community tanks and set up the quarantine tank with water from the community add the sponge and instant quarantine tank. It depends on how often you will be adding fish and how much room you have.
Regarding meds to keep on hand. I wouldn't bother, you can get it when you need it. Would you know how old it is other wise. Medications strength can change with time, hence expiration dates.
Prevention is the best medicine, by not overstocking and overfeeding. Frequent small water changes. Clean water keeps the fish healthy. Providing compatible environments, so the less stress the stronger the immune system. Another good investment is a UV sterilizer, it will kill many fish diseases. But even with a sterilizer, a 3-4 week quarantine is the best medicine, especially for your existing fish. I work at a vet hospital and one of the exotic vets visited who also does tropical fish, and she reccommended the sterilizer and quarantine tank.