Stay away from a PVC liner. The price might lure you in, but they are horrible. They get brittle in a matter of months and puncture easily.
You want EPDM or HDRPE. EPDM is rubber and reminds you of a tire inner tube. HDRPE is stiffer than EPDM, but it's supposed to be very durable. There's also HDPE, but it's not reinforced like the HDRPE.