I took a rescue 3 class this spring and the big take away I had was the large mouth bags are MUCH easier to repack, and I like to keep a bag on my boat and a waist bag also.
I use the Salamander Retriever throw bag. It has a quick release buckle, you can choose your rope, and also comes with a 9' tow tether and carabiner. My favorite raft bag I keep close by is the Cascade Outfitter's bag, my gorilla fists fit in there easily. If I was going to make my own bag, I'd pick my rope and use that bag.
Wishing I was on the river instead of surfing the web...