I would start with some sort of rust converter before I put anything down. Sand the rusted metal as much as you can then cleanup and apply some rust converter of some kind. This will seal the metal and prevent more rust from occurring.
If it was me, now you don't have to do this part, but, if it was me I'd spray some Black spray paint down first just to cover the rust converter. I know it stinks but, it would just be an extra barrier.
Then I would invest in some sort of vehicle insulation or for best results "Dynamat" Dynamat is expensive but, gives you the best quietness inside your vehicle. Helps keep noise out and inside noise in. Then lay your carpet on top of that.
Happy carpeting.
