What's the best insulation to use and to what depth. I'd prefer to
over-insulate than under-insulate. It is a lathe and plaster ceiling
and part of the roof has floorboards.

The best, but not cheapest method is to use rigid Celotex or Kingspan
boards. These provide much greater levels of insulation per thickness than
rockwool and don't disintegrate into a lung infesting mess. They are,
however, more expensive. Wear a respirator and gloves when removing the old
filth and take advantage of the work to thoroughly vacuum the loft.

Consider what your vapour control strategy is. When insulating, you should
have a vapour barrier beneath, to prevent hot moist air becoming cold
saturated air and leaving mould causing condensation soaking the insulation.
The problem would be much more apparent with fibre based insulants.
Normally, this is done using foil backed plasterboard, but this isn't
suitable for a new build. The best solution in retro-fit applications is
often to lay large sheets of plastic sheet between and over the joists,
taping up any holes you need to cut around struts etc.

Finally, consider the effect on electrical circuits. If you only have
lighting circuits up there, these aren't likely to be a problem, even if
derated 50% for insulation burial. This is because lighting cable is usually
seriously overrated to begin with. However, 2.5mm cable for ring mains is
much more marginal to begin with and may be a failure if buried in
insulation.

Christian.