Straight lines in plastic sheet are easily cut by scoring and snapping. Place a straight edge and draw the knife along it. Make several with a moderate or light pressure, especially the first one, rather than exerting too much pressure on any one cut. Then just bend it along the line and it should snap quite cleanly. For thicker sheets where you have to exert more pressure to snap it you might want to rest it along an edge.
For a knife I like a scalpel for most purposes. Most of mine are by Swam Morton but I do not know if these are available in the USA. The number 10a or 11 blades are probably the most useful. If you lean too heavily on the blades they will snap.
An alternative to a knife is a plastic cutter. Olfa make one as do Tamiya (I believe the blades are interchangeable between them). It is a useful tool but not a vital one.
Of much more use is a steel ruler. A plastic or wooden ruler will get damaged eventually and a steel one is not expensive.
Curved lines are much, much trickier. You can cut along an edge, something like a French Curve and you can get swivel headed knives, though I have had one for a decade or more and have never used it. For circles you want a circle cutter.
A fine saw is another useful tool. You can get fine ones that fit into an X-Acto knife handle or jewellers saws which are like a very fine fret saw. These are particularly good for converting figures.
Brass and plastic tube and rod needs a small pipe cutter. The one by K & M is small and cheap. A saw is not very good at cutting the pipe. For the finer diameters you can roll it under a knife blade and snap it though I find this quite tricky to do just right.
Plastic sections can be scored and snapped just like plastic card.
The basic tool kit.:
Knife (scalpel)
Steel ruler
Needle files
Fine sandpaper
Liquid cement (in a bottle not a tube)
Also strongly recommended:
Circle Cutter (Olfa)
Pipe cutter (K & M)
Right angle square, steel
Plastic Cutter
Clamps
Superglue, thick, viscous
Materials
Plastic sheet in various thicknesses
Brass tubing (K & M)
Fine brass rod (K & M)
Plastic tubing, rod and sections. That by Evergreen is very nice. Addictive to use – you keep finding more uses for it.
Textured plastic sheet (Evergreen and Slaters)
I hope this helps,
Michael