A friend and I made one of these when we were 15, back in the late seventies. We used silicon to seam the plexiglass and nuts and bolts to hold it in place. We also went to the local hardware and bought thirty feet of aquarium hose with the proper barb fitting and for a air supply line. We hooked the other end to a normal bicycle pump. We drilled holes around the bottom of the helmet to tie milk jugs full of mud to them. Four gallons of mud seemed to be the proper weight. We had a lot of fun using it in the local lake off the floating dock. We also hooked up a recovery rope to the helmet. We didn't strap it on to ourselves. We used an old garden hose to line the shoulder cutouts. Our helmet was an wet entry type, you had to swim underneath it to get into it. We took it down to about 25 ft.
Never made it to Phase Two which would have external lights on it.
Hope these memories give you some good ideas.

With out weight to off-set the buoyancy of the air in the helmet, you will only be strapped to a bobber. You will either need a huge weight belt (very uncomfortable) or weight strapped to the bottom of helmet. Here is another instructable for reference. https://www.instructables.com/id/Homemade-Diving-Apparatus/

For helmet material I'd go with transparent aluminum...

You know, the last picture reminds me of those nuclear safe suit helmets.

I'd put more like 360o on the transparent-stuff, that will collapse a bit too easily I think.

L

You could have made the clear "porthole" viewer a double walled thin aquarium. Use silicone caulk and some rubber sealed toilet tank bolts to clamp on some pieces of acrylic. Fill the middle with some of that lava tank stuff with the floating object or a real marine environment. You can then pretend to take the kids to seaworld without paying the exhorbitant amusement park fee.

Can you get the bends if you get off of your easy chair real fast?