Tap Plastics on Van Ness does exactly this sort of thing, and does it well. More on reddit.com

You could also use polycarbonate instead of acrylic (as ohtobiasyoublowhard mentioned). I would recommend polycarbonate, as it's much tougher. Acrylic is really brittle and can shatter, poly not so much. Look for Lexan or Makrolon, or various other brands of polycarbonate sheeting. For gluing poly, you can use methylene chloride (also known as dichloromethane, sometimes sold at hobby shops as "di-clo"). Again, straight cuts are a must. For cutting, if you're doing acrylic, it's tricky to cut good straight cuts without shattering the plastic if you're using any sort of saw. This is why I recommend polycarbonate, it's much more forgiving. If you are good at cutting straight lines with a razor blade, you can score (some) polycarbonate and then snap it. If you are using Lexan, you probably won't be able to score and snap it, that stuff is impervious to damn near anything. If you get some Makrolon, if you score to a depth of about half the thickness of the sheet, it snaps fairly easily. Round razor knives, a steel ruler, and a clamp work really well for scoring Makrolon. Clamp the ruler and the plastic to a table, then run the razor along the edge of the ruler, pressing down fairly hard. This can get you nice straight cuts that can be cleaned up with a bit of sandpaper, a dremel, or a file. You can also cut polycarbonate with a jigsaw or a circular saw. If you use a circular saw, and are tearing up the plastic, try turning the blade around backwards. It melts through instead of chopping through, getting cleaner cuts. Once you have your cuts, sanded flat, then put some methylene chloride on the edge, and clamp it down. Let it sit for a while, the solvent will dissolve the edges, and once it evaporates, you should get effectively a single piece of plastic. Good glue joints are see through, if you do it right. However, as you said you don't have any tools, so unless you want to do a lot of hand sanding and trial+error, I would really suggest getting a laser cutting service to cut your parts for you. A quick google search turned up http://www.customlasercutting.com/ which seems decent, though you can always shop around. They do acrylic, which although I'm not a huge fan, it will be perfectly fine if you don't play soccer with your cases. You can get them cut so that they have interlocking tabs, or just square pieces. If you don't have the means to make CAD files, go sign up for the Autodesk Education Community and you can download Inventor to help you make your files. For lighting, my favorite is always an LED light wall. Using a 0.25" piece of acrylic or polycarbonate, drill 5mm (or appropirate size, depending on the LED) holes perpendicular to the main planar surface (along the edge). Sandblast the plastic to get a frosted effect, then stick LEDs into the holes and power them up. The sandblasted plastic will diffuse the light, causing the whole surface (or a specific design, if you choose to sandblast only certain areas) to light up. If you want to know what I mean, just google for "LED edge light." More on reddit.com

You can make your own cheaper. Its not difficult, and then you don't have to hope for the right size.

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You can usually get glass or perspex cut to size cheaply, or particularly with perspex it's easy to cut yourself. 3mm thick in either is common. Perspex is a good option as lighter than glass and a bit easier to work with. Both can be joined with clear silicone or you can get timber for a frame - either square stock and route 3mm channels or you can get L profile and glue the glass/perspex inside. Them fit to a wood base. More on reddit.com