Should I buy a thermoelectric cooler or a compressor cooler?

Skip the thermoelectric coolers. You want a compressor cooler — it can freeze stuff and hold temperature even in a hot car. Thermoelectric coolers only cool about 40°F below ambient air, so on a 90°F day they struggle, and in a 120°F car your drinks go lukewarm. Compressor coolers from brands like Dometic, Iceco, or ARB cost $400–$1,000 but last a decade and actually work.