I assume you're talking about solvent welding, not welding with heat and pressure. Polycarb and acrylic are usually welded with a dichloromethane containing compound that contains some of the plastic monomers. PVC uses a solvent that cleans this plastic first then some MEK to weld it together. Check out the individual plastic manufacturers' or solvent manufacturers' web sites. This is also a good resource:
Solvent welding with methyl ethyl ketone (MEK) or toluene is the most economical. Next least expensive is a hot melt adhesive such as ethylene vinyl acetate (EVA) or ethylene acrylic acid (EAA). The most expensive would be an adhesive such as cyanoacrylate glue.