For cell cast acrylic, Plexiglas-G and Acrylite GP, or Polycast ($$).
For extruded, which you can do, it bonds the same but might bow more over time, Plexiglas-MC or Acrylite FF, or any domestic equivalent (stay away from import, if possible).
You can also try to find something called PMACS which is Plexiglas' cell cast product to complete with the imports, it's generally the same as the G stuff and that's what I use for sumps.
For rough cutting, I use a plastic cutting blade, Diablo, at Home Depot (triple-chip blade) and you could do this and then manually scrape with a razor blade to get bondable edges, or use a jointer or router table for the best edges. Squaring the ends or keeping them equally "off" is probably the most important step IMO
Bond with weld-on #3 or #4 and use the pins method in conjunction with foam-covered boards and shims
Clean edges with denatured alcohol and blow off with compressed/canned air before setting the joint
use 90 degree angle brackets to hold parts in place and let joints sit overnight or longer before touching.
That's the quick and dirty. There are a lot of details to fill in but that's the basics.