If there's water or excessive damp in the footwells I'd investigate further and check for any leaks first before you go replacing any carpets.
I'm in the process of doing the same in my mini, although slightly different. Firstly I took up the carpets (but didn't actually remove them, just folded them up one footwell at a time) and inspected the floorpans. As with you there was slight surface rust but nothing major. So I sanded off all the surface rust to bare metal... and painted over it with Black Hammerite.
I did this on all the floors including the boot floor. I then painted over it with some Poly paint which nearly matches the body colour just to make it look nicer (and give it a little more protection) but if you want to leave it black then the Hammerite will do fine. I did that on my old mini
I'm going to use normal carpet underlay on my new carpet too. Got it from a local carpet warehouse today, they had some odds and ends, managed to get enough to put three layers of underlay in the whole car for £25

it sounds a lot, but it is only about 1cm think and the standard sound deadening stuff is a lot thicker I believe.
I plan to just glue the underlay to the floor with a normal carpet adhesive (aerosol form) and to the other layers of underlay. The new carpet I have has got quite a "grippy" back so should sit on top of the underlay nicely.
I will be updating my project page (blue link in my signature) as I fit it...