Your questions are a bit broad, but I'll give it a shot anyway...
Styrene for the modeler comes in a couple of forms. Often it's already been injection molded to resemble a plane, tank, or car, and put in a box. For those of us who care to scratchbuild, we buy extra strips or sheets (also preformed; see the catalog at the link you attached to see some of those available), and cut them up for use as we see fit.
The properties of these materials are somewhat size dependent. For example, thin pieces (0.010") have a stiffness comparable to construction paper or manila folders, while thicker pieces (0.040") can have a stiffness comparable to the cardboard on the back of a notepad.
If all you're going to do is flat sides/straight sections, just get the plastic, cut it to size, and glue it up. If you're going to need to do curved rails, then things start to get tricky... thin plastic may hold it's shape or be bent easily, but thicker pieces may need to be heated (not melted), shaped, and then allowed to cool.
Likewise, if you want to do curved side-panels, you may have to carve masters and vacuum form, a la the 2nd link below:
A relatively simple project: http://www.briansmodelcars.com/tutorials/tutorial.asp?TutorialID=32&CurPage=1
A more complex project: http://members.aol.com/GCGassaway/vacuform.htm
Evergreen Styrene and Plastruct are the more common brands I've heard of, but the stuff you've mentioned will also work. My personal preference is to go to the hobby shop so I can eyeball the stuff before I buy it, but that's not always an option.
Basically, a lot can be done with styrene, though it's usually a matter of time and patience.
Painting - I would recommend enamel or acrylic based paints. Some use lacquers (usually auto builders), but they're pretty nasty and require some extra processing.