Mr Engine, essentially you have 2 potential problems with sound proofing and you need to assess what type of soundproofing problem you have. This is not too difficult to do and will save you money and time in the long run. Easiest way is to put a loudspeaker in the cellar and crank it up with a bass heavy track, use a typical sound level which you expect to use. Go upstairs and listen to what you can hear, if its bass you have some structure borne issues. If you can here treble then you have an air borne issue. This is hugely simplified, but gives a start.
Air borne issues will be resolved with what you have suggested, some mass from the plasterboard and rockwool, just make sure use plenty of sealant to make sure you get no flanking paths (short circuits such as a pipe going though a hole etc).
The bass issue is more difficult to resolve and mass is what you need, several layers of plasterboard, even the heavy types should be considered. If you have a big issue then barrier foam can also be fitted between joists and false ceiling, this is a 95kg/m3 foam so you going to have issues holding it up. The final problem with structure borne noise is that and solution you use should ideally float, not easy to achieve!
Hope this gives you some ideas, but try the experiment and go from their.
Dupe...