I thought long and hard about this very question and opted for a conventional "Coleman type" beer/wine cooler with a carrying handle. It is outfitted with one inch foam around the sides and bottom, which I already had in the garage. Due to my unique circumstances, I needed to take into consideration leaving the case on the shore in a high traffic area known for the disappearance of small boating items like life jackets, cushions, etc., or put it in my small boat.
Thinking a Pelican-type case would be nice, but wouldn't last long left unattended and because I did not want another storage device competing for space in the boat, I opted for the throwaway cooler. Now I just leave it empty hooked to my small dock and if somebody wants it, they can have it because I could get another one at a garage sale for a buck.
I also tuck it behind the driver's seat in my truck when traveling and don't worry about my HB getting wet, either. Plus, there's room enough for the ram mount, too.
It's kind of surprising to my wife that I went with this option, because I am known to be a little over zealous in the affection towards my other significant other a/k/a Amazon.