Cooler size is dependent on what you're using it for. It needs to be big enough to hold all your food and beer that needs chilling, plus ice. About 1/3 of the available space goes to ice (variable with how long you need to keep things cold).
You want the width of your cooler to be the same size or smaller than the gap between tubes. It's okay if the cooler slightly touches the sides, but you do not want it pushing the tubes out. You also want to suspend the cooler off the floor. If you don't, then the heavy cooler will push the floor down, changing the performance characteristics of your raft. It will also make your floor more vulnerable to damage (think rock and hard place). With the cooler suspended off the floor, the floor can mold and push up when you go over rocks, helping to minimize damage to the floor.
Also, I like marine coolers because they tend to seal better. This helps keep things cooler, and helps prevent river water infiltration. Marine coolers also tend to have stainless steel hinges, bolts, etc. to minimize corrosion and improve longevity.
"A witty saying proves nothing."
- Voltaire (1694-1778)