Honestly , I would use glass. I have been reading tales of the beardies scratching at the doors and plexiglass scratches easily and I wouldnt do screen , might be hard to keep temps right. I plan on building a cage too and I will use glass, 1/4 inch thick.
As for the hammock, you can get those plastic 3M hooks and use them, thats what I will do .
almost everyone uses plexi. There is more of a risk of it scratching and of course clouding in time from the lights and heat. I'm having mine built by a friend using tempered glass front doors. More expensive, for sure, but I shouldn't ever have to replace them. The plexi is also a lot easier to actually build the door with if you don't have a glass guy to do the cuts for you. I can't comment on either's ease of everyday use, since mine are still being built, but I'll weigh in on behalf of glass very soon
I have used acrylic (plexi) in all my vivs. I like it because it is lighter than glass and you never have to worry about it cracking or chipping. I often pull out the doors on mine to clean and don't have to worry about them breaking. For the hammock I would use teacup hooks... you will find them at a michael's or Joann or any other craft store. They are far less bulky than other things.
My viv has glass sliding doors, and sure enough putting them in placed the corner got cracked
Both have positives and negatives, Glass WILL break if your not careful but your beardie will never be able to scratch it,
Glass also keeps the heat in better.
Plexi isnt as expensive but is scratchable. Although it wont cost that much to replace if it does
Take a pick