The type of material your woofer is made out of depends on the sound quality you are looking for and how much money you are willing to spend.
Paper (pulp) woofers are the least expensive, but if properly engineered can provide great sound. However, they should not be overused in car speakers because of their susceptibility to moisture.
Poly / Plastic
Possibly the most-used material for car speakers, poly and plastic are weather-resistant and have good internal damping.
Mica, CMMD (Ceramic Metal Matrix Diaphragm), Glass-imides, HCL (Honeycomb-Laminate), and IMPP are all types of composite materials used for speakers cones. These materials are non-resonant, stiff and strong. They all create uncolored sound with excellent dispersion.
Cast metals have greater resistance to resonance than stamped metals. Cast aluminum is not only lightweight but also very strong.