Cover the ceiling and cover the floor (carpet) if it is hard surfaced, as these will transmit the vibrations too.

The best is to build the structure Gervase suggests with no attachment to the existing, leaving a space between. If you want to go as cheap as possible at first, with the ability to upgrade later, build the frame and cover both sides with polyethelene, that cheap plastic sheet used for a vapour barrier (don't use an air barrier as it will not work as well... sometimes, these are confused). Again, bare poly is deadly in a fire. A substitute for planking is Gypsum Board. Is it common where you are ? Round here, it's the cheapest thing going, it's easy to work with, and it provides fire protection. If you need any construction details, I will be happy to provide them.

Overall, I suppose Paddymac has provided the best alternative on a cost-benefit basis.