I have dogs, so I made a polyester pad (you can't really call it a quilt, although it is quilted, so maybe you can!) for the back seat. It catches shedding hair and stuff they pick up on their paws. They seem to like the bedding material it provides. I shake it out regularly and throw it in the wash once in a while. It's eight years old and still looks new.
I think you've got the right idea, using the poly where durability is an advantage. Cotton is more comfortable against the skin, but padded poly is more comfortable than the floor!