i run Tank Transfer Method (TTM) and then several weeks of observation in a grow out tank which is a 20L.
i typically use 10 gallon tanks for my TTM tanks. they're easier to work with, carry, clean, etc... they also don't take a ton of water to fill. i keep two 20L around for larger fish i want to run through TTM, but so far the 10 gallons have been sufficient for a wide range of fish, since they only spend about two weeks in them through TTM and their prazi treatments.
the grow out tank is fully cycled, with a skimmer, so that's just a regular setup. i don't treat with any kind of meds in it, i would use a hospital tank for that. for the TTM tanks, i use amquel so help keep ammonia locked up, and since you're transferring about every 48ish hours the water stays clean enough, long enough. with the exception of some super touchy fish, this has done well for me. if the fish are really sensitive, then i will also do a 50 - 75% water change on the TTM tanks every day to help keep things clean and pristine, siphoning out uneaten food with it.
or....
HOB filter can work well for short term qt setups. if you have access to a fully cycled system you can keep some extra filter floss or sponges in the sump to use in the HOB filter. conventional wisdom is two weeks in the sump for media should be sufficient to help seed it with bacteria. you can also use aggressive water changes in conjunction with amquel (or another comparable ammonia locker product) for the duration of the QT.
i would probably not return the media to the main tank after qt, i would likely just toss it out, especially if you treat with any meds.
i also keep some cheap salt around for QT, regular old instant ocean, since it's fairly cheap and i throw out a lot of QT water.