The type of material used for a surround really depends on your goals for the driver. There are also various types of foams and rubbers. The old foams were polyester foams, think the old polyester clothes of the 70's. This is the cheapest foam to make, but it can deteriorate due to UV rays and other environmental issues. On the other hand it is also the most well damped and free from resonance. Our Lambda woofers use polyester foam for the damping characteristics, and then we hand seal and coat both sides with a damping component to further damp resonances, seal them so they are air tight, and protect from UV rays. For a driver to play up over 250hz, this is really the only way to do it. The newer foams are polyethylene foams. These foams are much more expensive to make, but are more chemically resistant, resistant to UV rays, etc. In general they last longer but they have more issues with resonance. For subwoofer use though this is not an issue.
For rubbers there are many types. Butyl, NBR, EPDM, Santoprene, etc. They all have typically worse damping characteristics than the polyester foams, and with rubbers it is very hard to apply anything to further damp a resonance. On our AV woofers we use the santoprene. This is the most well damped of all of the rubbers and also has the best temperature range. Other rubbers become brittle at higher temperatures than santoprene. I believe santoprene is good to -60F. Butyl and NBR will be more likely to crack in cold northern winters if you don't let your vehicle warm up first.
John