I agree, bigger is better. You can never have too much ice OR beer. And on day runs or short trips, you can use it as dry storage. room for a small cooler (soft sided work best) and extra gear like pump, repair kit, first aid, etc...
also, if funding allows, invest the extra money for an upper end one that has a sturdy lid and hinges.
I usuall take 2 coolers. a dry one for food and a wet one for beverages.