MDF = Medium Density Fiberboard. Home Depot has it in 4'x8' sheets. About $20. Unless you're building something huge, that full sheet will be enough, but figure out the dimensions of each panel for your box ahead of time because they'll cut it six times for free and then $.25 for each additional cut. So you can have them do a lot of the work for ya...not to mention making it so that you can get that 4'x8' home without a truck.
Sealant of choice on many forums would seem to be Liquid Nails or an equivalent. Screws every two inches or so also. Silicone isn't going to stick very well to wood or plexiglass. At least not well enough to stand up to the pressure inside the box.
From what I've seen about plexiglass, you'd need about 1/2" or better, which is quite expensive. And it is a PITA to work with and have it look good.
I'd suggest finding a big cardboard box and hack it up and build your enclosure out of that so that it fits in the car like you want and you get the internal volume that you need. That's what I did. Lots of measuring and trimming and recalculating in MS Excel.
I've got pieces of MDF sitting in the corner right now waiting to be trimmed and put together.
