For qt/hospital I use a bare tank, a HOB filter for water movement and a sponge I have stored in my sump to collect bacteria for this use, a heater, and some pvc pipes for the fish to hide in.
You don't want to use sand or rocks. If you don't have media don't let that stop you, you can still set up a hospital and do frequent water changes.
If you use copper you'll need a well known brand such as Coppersafe and the appropriate copper test kit (there are different types of copper treatment so be sure you are testing for the right kind, chelated, etc). Follow the directions exactly.
If you use hyposalinity you'll want a refractometer versus a hydrometer to be certain you are getting accurate salinity readings at such a low level (around 1.009 although I've heard of some only going down to 1.014)
You won't need to remove anything else from the display tank, but you will be trying to remove the parasite and will do that by allowing your display to go falllow for 6+ weeks.
How big of a tank you'll need is dependent on the size and number of fish.