Silicone caulk is probably the best adhesive for glass. I guess it would work for plexiglas too, but there are better, easily available alternatives.
For gluing plexiglas (or other forms of clear plastic sheet; "Plexiglas" is in fact a brand name) you really need a solvent adhesive that's designed for the purpose. Check the label of whatever liquid cement you normally use for building models; some of them (e.g., Weld-on #3) work on plexiglas. (Others - e.g., Testor's - don't. The label should make it clear. If it says the glue works on acrylic, you're in business.) If you don't already have any appropriate stuff, you can probably buy it (it's not expensive) from whatever dealer in your neighborhood sells plexiglas. (I believe our local Lowe's carries it.)
One word of warning: plexiglas butt joints made with solvent are quite sturdy IF the plexiglas is sufficiently thick. The handbooks generally suggest that you don't try it with anything thinner than 1/4" plexiglas. I've gotten satisfactory results with 3/16"; at that thickness the joints have occasionally come loose in spots, but have been easy to fix. I wouldn't recommend trying butt joints with 1/8" plexiglas, unless the case is extremely small.
The basic technique relies on capillary action. The edges of the sheets need to be cut accurately to size, and the edges need to be cut at, or mighty close to, 90 degrees. With a table saw, that's easy. If you don't have a table saw and are using the "scratch and snap" method of cutting the plexiglas, have the guy who sold it to you sell you a scraper and scrape the edges till they're square. If they're at all rough in texture, rub them with a fine sanding block; the smoother the edges are, the better your joints will look.
Hold the two pieces firmly together in exactly the positions you want them to keep. (An extra pair of hands will come in handy.) Then apply a few drops of the adhesive to the joint. A syringe of some sort is the best applicator; some brands of glue come with needles built into the bottles. A small brush will work if you're careful. Let the adhesive flow into the miniscule gap between the pieces. Then hold everything together tightly until the adhesive dries - which will take five minutes at the most. Repeat the procedure for the other joints, and you'll have a vitrine for your case.
If any of the adhesive goes astray, leave it alone till it dries. If you try to wipe it up, you'll make a mess. Let it evaporate, then - if the damage is visible at all, which it may not be - polish the spot with a damp cloth dipped in automotive rubbing compound (or, in the case of really minor damage, toothpaste).
This is a sort of rough-and-ready method of making plexiglas joints. The corners almost certainly will show some bubbles and other flaws; to get a really smooth, shiny butt joint in plexiglas requires the fancy, highly expensive equipment that the pros have. To my eye, at least, the rough-and-ready method works better with larger cases; in a big case, the little flaws in the corners don't attract nearly as much attention as they would in a tiny case.
Hope that helps a little. Good luck.