Best insulation for ground floor above cellar?

[TheMitchells]

In our renovation property, we have been having problems with damp in the cellar (who doesnt!).

One corner was particularly wet with droplets of water on the Rockwool (I think) insulation shoved between the joists of the lounge floor. We have removed the insulation and increased ventilation of the cellar and plan to fit another airbrick in this corner. The back corner has one and isnt damp at all. 

Then as part of the renovation, we are either going to replace the joists as most of the ends are rotting where they sit on the external wall.  The Structural engineer suggested that we could just cut off the ends and attach new lengths, which will sit on new engineering bricks on dpm on the external wall.  Hopefully that will prevent any dampness in the new joists. 

My question is how to insulate the floor so the lounge is not subjected to draughts from below.  I am loath to re-install the Rockwool as I am sure that was causing some of the problems.  But we need some sort of insulation.  Is there another good insulator that isnt going to cost the earth to pack between the joints or should we look at laying insulation above the joists with the problem than of raising the floor level.  This may not be too much of an issue as we have to re-do the floor in the whole house anyway.