Hello; The usual description is that the large bulk of the beneficial bacteria (bb) will be found on the surfaces of things in a tank and much less in the water itself. This makes sense to me as well. It is also often suggested that you keep such material wet during the change in order to keep the bb alive. The bb are living organisms and will begin to die off when their nutrition is removed so the move into the new placement of the tank should not last any more days than necessary.
Keeping some of the old tank water may help prevent some shock to the fish in the event that your home water is chemically different. It is my understanding that the water itself is much less important for maintaining the cycle than other things such as filter media, plants and decorations. If it becomes too much of a chore to keep a lot of water the fish can be acclimated to the new water much as you should do when bringing them from a fish shop.
Bringing a used tank in and seting it up right away with the old substrate and materials would depend, to me, largely on how nasty the tank and material happened to be. I generally like to clean up a used tank and the substrate and set it up freshly cleaned. Is it possible to keep the fish along with the filter medial and stuff in a short term container while the tank is being prepared. Do you have an already established tank that bb loaded matrial can be pulled from?
Good luck
