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 or tackle bags is to go light and give you freedom, carry some fishing tackle and tackle boxes. The bigger bum bags or tackle 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.
A bum bag are basicaly tackle bags to carry your fishing tackle fly boxes provisions to carry water are also important.