New false ceiling. What type of insulation?

[bazmo]

Hi people. 1st post as I'm just getting started in the DIY game.

I'm putting a false ceiling in my bathroom in my ground floor flat. The original ceiling is just plasterboard. I've constructed a frame 150mm below the original ceiling to support the cladding that I'm planning to use on the new ceiling.

What material is best to insulate the cavity I've created?
Would it be worthwhile insulating the original cavity between my old ceiling and the floor upstairs, or is that just overkill?
I'm planning on using downlighters recessed in the new ceiling, would this make a difference to the type of insulation I should use?

Ta