There’re many variables on how to setup a QT/hospital tank and, really, the choice will be up to you.
Personally, the Rubbermaid setup, I don’t advise. The purpose of a QT/hospital is, as in the case with a QT, to observe fish health and behavior. How do you do this in an opaque container? Likewise, in a hospital, while you may know before you put your fish in a Rubbermaid what disease your fish has and how you are going to treat it, you will still have the same problem of observing progress, deterioration, or, as is the case with many disease processes, the onset of secondary infection which you will need to subsequently treat. How do observe fish is plastic containers?
Yes, you can use a QT as a hospital tank, however, once you use the tank with medications in it, you should be cautioned about housing inverts or live rock in it unless you completely break down the system and clean it. This is particularly true if you use copper, as copper can adhere to the sealant or glass of aquariums, then leach out into the water once you fill the tank. Inverts have no tolerance for copper, or most medications for that matter.
You can setup a permanent hospital/QT and keep it established and available at all times, or you setup temporaries as you need it. The filtration is really your choice. Biological filtration will establish in a tank that has any organic material in it. On the glass of your tank for instance. True, it will not be in the volumes that you find in an established aquarium. If you want, you can filter your QT/hospital with a canister filter. I find this handy because, more so in a QT and hospital, you will be doing more water changes. This is easily accomplished by just working with a canister, rather than removing water directly from the tank. Additionally, the canister can hold carbon, which comes in handy when you want to clean up the tank following medication therapy. But, as I said, any filtration will do.
In a temporary setup, one where you are using your QT/hospital for a particular at the moment need, you obviously will not have a cycled tank. Here you will want to use good quality water from your main tank to help with cycle. You may also want to put in a cup of your substrate to assist with the cycle. In this situation it will be necessary to constantly be testing your water. You do not want the temporary setup to cycle, so you will have to be making frequent water changes. This is actually a plus because your fish will benefit from the water changes. Really, when setting up a QT for a new arrival, you can certainly setup a wk or 2 in advance and get the tank established by supplying it with a organics yourself—ie: a piece of fresh shrimp.
One thing you will need to do if you go with a aquarium setup is to paint the bottom of tank [on the outside] black. This is done because you should not put substrate in a QT/hospital. WO the substrate, the bottom of the tank is very reflective--a stress situation for fish. Additionally, you will need to provide comfort zones for your fish by placing either fake rocks or PVC pipe---places for them to hide.
