A lot of people don't cycle a filter and primarily rely on frequent water changes. Some meds will screw with your bacteria and/or require lots of water changes anyway.
I did cycle a filter for my quarantine tank when I was stocking a new tank, but that was because I knew it would have fish in it for a few months as I added different groups. I did need to treat for ich with one group, but most of that was just observation and no treatment. I keep new fish in quarantine for month because I don't want pathogens in my display tank.
I've never needed a hospital tank for my established fish, though I guess there are cases where it could happen, like an injured fish. I don't keep a filter ready just in case, no.
<"Good advice">, also if you have floating plants you can transfer them to the new tank and they will start improving water quality straight away. I actually mainly just swap over <"the big intake pre-filters now">. They are cheap to buy and I just make sure I always have a couple of spares to hand.