To answer the actual question originally stated...
PolyCarbonate
1/8" will be fine as long as all of your edges meet. 1/8" is still rather flexible and has a moderate amount of give unless you secure it properly. This is also the standard thickness and is easy to get ahold of a Home Depot in the window/door section.
It will be under the BRAND NAME Lexan.
1/4" would be required if you were constructing a case the size of a full tower.
1/2" would be ideal for bracing pieces since it is thick enough to be tapped for screws.
Acrylic is too weak for case construction. It's original usage is for application that require optical clarity, low material weight, and scratch resistance. The sheets available at hardware stores are only meant for use in greenhouse construction. This is why the sheets are exceptionally brittle.