What kind of cooler should I use in a truck bed?

You need a rotomolded cooler. Injection-molded ones crack under heavy loads and turn chalky white in the sun within a year. Rotomolded coolers (Yeti, RTIC, Pelican, Canyon) handle UV rays and can take a 200-pound person sitting on them. I’d pick RTIC over overpriced Yeti—spend the savings on ice.