Insulation is a tough area. There are people on here that know a lot about it and hopefully that can guide you. A couple of comments ...
How deep are the rafters?
Is there no existing blanket or foil under the tin? This could be a challenge, it can be retrofitted from below for thermal purposes but that will not help drain condensation.
There is a lot of discussion about whether sound rated insulation and plaster is worth the extra money ... or is it like the price hike that comes with putting the word 'wedding' or 'baby' in front of a a product?![]()
One key thing for sound is that it will find any gaps and undermine your whole plan, so whilst it's open it'd be worth filling any holes with filler, foam, etc. to help seal it out. The way I think about it is ... sit in your car (you don't need to be moving) and it's fairly quiet, open the window just a crack and all of a sudden you have all the outside noise, open it fully and you have only a bit more noise. The point being that the tiny crack let in the majority of the noise. It's not the whole solution but it's cheap and easy whilst the roof space is open.