Slow,
I used to fish out of a belly boat and enjoyed its many advantages. Being able to put in just about anywhere and the convenience of its small size are real pluses. And, the thrill of hooking a fish that will pull you around is something not quickly forgotten!
It's not for the faint of heart, however. Wondering if a snake is going to come closer or if a beaver is going to see you as a threat... or, bumping your leg on a limb or log where you least expected one will keep you on full alert. Pulling up your stringer to find an angry turtle attached to your catch is also pretty common, at least 'round here. Always a trade-off.
I've never tried using diving flippers but know a lot of guys who do. I have a set of flippers that have a heel cup, you strap them on over your tennis shoe, a flipper is hinge-mounted on the outside. Kick your leg forward and it swings back, kick back and it extends and you gain momentum. I've been very pleased with them.
During warm weather, I'd wear an old pair of cut-offs and canvas tennis shoes. During colder weather/water or where water moccasins were thick... a pair of thin, rubber chest-high waders with shoulder straps.
You'll want to have either a zippered pocket on the tube cover or a small tackle box with straps, a strap-on rod holder is real handy also. I know a lotta guys who've sent rods to Davy Jones locker while float tube fishing. Beer may have been a factor, though.
I have a mini-pontoon also and use it more now. Much more comfortable and safer, I think. It doesn't take up a whole lotta room. It has the inner air bladders with an outside covering and I have to adjust the air pressure now and then. It's far from being the best rower and a moderate breeze will push you towards the shore in a hurry. I could mount a 12 volt trolling motor/battery on it but haven't tried that yet.