If it’s a genuinely suspended floor i.e. with a clear void between the ground and the underside of the joists, then you don’t have to worry about moisture soaking the insulation.
PIR (e.g. KIngspan) insulation will give you much better U-Values than mineral wool (Rockwool/Earthwool) and can be friction-fitted between joists, or supported on battens fitted to the existing joists. I prefer Rockwool as a product because it’s essentially molten rock spun to produce the fine fibres (You get a very similar product occurring naturally at some volcanoes), rather than expanded chemicals, but they both have their uses. It may depend on the depth of your joists: If you have very shallow joists, then PIR insulation will give you the best thermal performance for the given thickness. However, deeper joists may allow you to use thicker insulation, which may suit Rockwool/Earthwool.
As others have said, mineral fibre insulation generally requires a wire mesh fitted to the u/s of the joists to support it.
The downside to PIR/rigid insulation is it needs to be cut to shape, which can be time-consuming. Mineral wool does as well but as it’s compressible, it is more forgiving when it comes to cutting to fit.
Rockwool, Kingspan and Knauf have lots of information on their websites, if you want to research it a bit more.