3/4" minimum. I used a sealant on one of my projects called Lexan*. IMO I would still use some sort of fastener to keep the box together but success has been achieved without it. Plexi is incredibly strong but hard to work with. (Not as forgivable as wood).
I also recommend having your pieces cut from the manufacturer. They can precisely cut it to within 1/64th of an inch or better. Clean edges too. That is if it's a standard box with 90 degree pieces.
You do realize that a plexi box and even a plexi window changes how the wave moves within the enclosure right? The enclosure you plan to build will likely have a very "boomy" sound to it.
U can use an acrylic solvent that actually melts the 2 pieces of plexi together. Usually they sand the edges to a 7 degree angle and the solvent fills the gap- so u cant see the joint.(Museum quality cases). BUT- best to have the plastics supplier fab it for you. IF ur just using ONE side for viewing, get at least 1" thick. Its like $40 a sq foot- but the thicker the better cuz u wont be able to brace it- if its a large surface, and IF u have to brace it- it'll look like a** to have wood screwed to it! COULD use real tempered glass- but dangerous to work with and have in ur vehicle.