It does reduce noise in the interior, and makes the car feel more solid. That's what the factory tar material did. I know the old tar stuff would get ugly over the years, and the floors sometimes rusted underneath it. But, the sheet metal floor, without insulation, transmits vibration and noise when left bare. Just imagine taking a piece of bare sheet metal and tapping it with a hammer. You know it's going to have a sharp, ringing noise. Now stick some insulation to it, and you'll get a quieter "thud" instead, since it deadens the vibration.
The type of insulation to use directly on the floor metal should be something that simulates that factory tar material. Nowadays, there are better materials than the tar. There are tar based insulations, like used for construction, but stay away from them, since tar can melt and make a mess when overly heated. And it can have an odor. Instead, the best floor insulations are made from butyl rubber, like Dynamat. There are other brands, but be sure they're butyl. Butyl doesn't melt or stink. Some people cover the entire floor with it, which is bound to make it super quiet. But, you don't have to cover everything to get the effect. If you cover most of the flat broad areas of the floor, that act like a metal drum, and stick a large square of butyl insulation in the middle of it, it will stop the drumming type of vibrations and noise. So, that kind of insulation is mostly for noise and vibration control. It will reduce some heat, but is mainly for the noise. It's the most important part of the floor insulation.
For heat reduction, an air barrier is used. When you buy carpet, it normally comes with a "jute" backing. This jute backing is a good heat insulator since it holds air in the fibers, and may be all you need, and you'd be done. If you want additional heat reduction, you could install some of that bubble wrap covered with silver foil over your butyl floor insulation, before installing the jute backed carpet. There are other products besides the bubble wrap for heat insulation too, like fiber or foam material, stuff that holds air.
I even like to stick some Dynamat to the inner surface of my door metal, underneath the door upholstery panel. They make some Dynamat that's thinner for doors. I use it in place of the paper water shield that the doors originally came with. Makes the doors sound quieter and more solid.
The floor won't rust if you prepare and paint it with good materials. While your interior is out, it's the perfect time of course. Strip the old paint and rust off your floor, and make sure it's clean. Then there are a couple of materials that are good. I've used both. My favorite is to paint it with two-part epoxy primer. This is real automotive primer that you'd buy from an auto body paint supply store, not spray cans. Spray it with a gun. Then spray some single stage urethane paint in your choice of color over the epoxy. Even clear urethane would be good. Or instead of epoxy, POR-15 over a properly prepared surface works good too. Follow the instructions for proper preparation of the metal for using it, so it will stick. It can be brushed on. Then use urethane paint over it too. Either of those would protect the floors better than what the factory paint did.
