For smaller fish I use a 5gal hermit tank. I keep this tank running on all the time, whether I have a fish in it there or not. In that tank I have live rock and basically when I do a water change on my reef tank I use the water in that tank. This works out really well for me and I don't think I've lost any fish from using it. Now, some people may not be able to keep a small tank running all the tank but you can have small pieces of LR in your sump, or a sponge filter, and then when you need to setup the small tank you can use those things as biology filter.
For larger fish I use anywhere from a 10gal tank to a 50gal Rubbermaid container. I don't use any biology filtration when I do this. Basically I try not to feed a lot and do big water changes, 50%, sometimes twice a week, and after that I will change all the water and then clean out the tank. I then start over with fresh water, usually from one of my tanks. If I see the fish has something I'll then start to treat. This has worked well for me over the years.