It's true there are many rabbit holes which you could jump down when talking about the right gear for the right fly fishing experience, but it's a safe bet that none of those rabbit holes are any deeper than that inhabited by bumbags. Preferences and opinions differ wildly.
Speaking from experience I would suggest to keep the size of your bum bag as small as possible. Lets face it the idea of a bum bag is to go light and give you freedom. The bigger bags are uncomfortable as they tend to drag down of your waist.
Make sure your choice has a shoulder strap this makes it more comfortable. Mine is waterproof as I wade the salt flats a lot and even in the fresh when wet wading I tend to get in a bit deep.