If you want to have a surface for biological filtration I would suggest using MarinePure products which you can bake to ensure everything is killed that may be in the pores after each use. Rock would take a bit of time to ensure everything was gone from it since you can't really bake it. Once you would bake the MarinePure you could put it back in the sump to repopulate bacteria.
Regardless of which one you use though, adding medication becomes difficult because they will pull meds in and thus make the actual medication in the water column lower than you think it is. Then post medication they will expel it back out. It is one of the reasons a lot of people refrain from using actual rock. Having a tank that uses PVC elbows rather than rock allows from a very quick disinfection should it need to happen compared to having rock in the system as well as no worry of medication being reduced in the water column.
What you have right now though will get you through a QT cycle with little headache as long as you monitor water quality. If you set it up as gone fishin suggested without "cycling" the tank it becomes very easy to set up a QT. The hob will help with the air exchange and provides an easy place for small amount of carbon or floss also if no meds are being used (I use a HOB and a small air input to agitate the surface).
Now, water. Here is my take on water. I use the water from my DT because I have QTed my fish in there prior to placing them there and the only risk I have would be the inverts/coral which would much smaller risk than a non QTed fish. My other thing though for using it is, I KNOW the fish will be going in the tank after the QT anyway so am I doing myself any good not using the water that it will eventually end up in. The reason I am QTing the current fish is to remove anything it could be carrying so it doesn't get in the system. Regardless, the fish will go in the DT water anyway so why not allow the TTM and QT to benefit the DT with small water changes? Yeah, very different thought than most but it is why I use my DT water. I QT to keep what the new fish is carrying from entering the system. Again, my thought process and people will argue it. The water that the QTed fish is in never goes back in the tank so it is a one way cycle.
Again, I am probably going to get heat for using the DT water with the reasoning I do, but when you get to the concept of it there is really little reason not to unless you have multiple system possibilities the fish COULD go into vs my one tank it will definitely go into.
The answer to your question TECHNICALLY is to use freshly made water.