Best glue for acrylic is solvent cement, which is a mixture of methylene chloride and other nasty organic chemicals. Weldon is a good brand, though there are others. You buy it at plastics suppliers (see your yellow pages) or hobby stores. It generally will not fill gaps, and requires very clean joints.
Next best glue is a gap filling cyanoacrylate (superglue) for plastics, generally available at hardware stores.
Third best is regular cyanocrylates (superglues).
Think about making gussets & other reinforcing blocks, rather than trying to make perfectly matching edges for gluing.
