To be honest, if you're thinking of constructing something out of acrylic, check out an industrial or plastics supplier. Their stock is often kept in better condition, and they have a wider selection of thicknesses and sizes. Plus, you'll likely need to get glue and applicators from them anyways.
IPS Weld-On makes decent solvent adhesives. You're also going to want an applicator bottle or syringe with a blunt needle - these can often be acquired from a well supplied woodworking retailer, hobby shop, or arts & craft store (Pearl Paint, **** Blick, etc).
In addition to solvent glue, you can connect acrlyic pieces via threaded inserts, machine screws, etc.
For cutting thinner panels, you can use a "score and snap" method. For thicker pieces, you'll need a saw, possibly with a special blade. I use a non-ferrous metals and plastic blade on my miter saw for the occasional acrylic cut.