Here are some things I do to make straight cuts.
My 'tool of choice' for making long or deep cuts in plastics is a razor saw with fine teeth (54 teeth per inch) and a blade that is 1 inch deep (the big one with the red handle in the picture).
Mark the cutting line all around the part using a pencil.
For a first cut I measure and mark points around the part, then connect the dots. In case of a complex shaped part a strip of masking tape applied with its edge along the dots may help as a guide to draw the line. If the shape tapers then apply the tape to the narrow side of the dots.
For parallel cuts I first mark points for both cuts, draw a full cutting line for the first cut and make the first cut.
Then I stand the part up on its freshly cut edge, make a stable stack of cardstock (or other suitably thin items) high enough for the pencil tip to reach the marked point for the second cut.
Then I hold down the pencil on the stack and gently rotate the part whilst touching the tip of the pencil until there is a line all around the part.
In case of plastics that are hard to mark I apply masking tape to draw on and draw the cutting line.
Making a saw cut through masking tape causes the glue from the tape to transfer to the saw blade, which makes sawing harder and more messy.
So instead I use a sharp hobby knife to scribe the marked line into the surface of the plastic and remove the tape.
I find this easier and much more accurate than using a marker pen.
To cut along a line I aim the front edge of the saw blade at the line.
When the edge of the blade lines up with both the level and the vertical part of line the cut should follow the line.
In the enlarged part of the picture I changed the color of the pencil line to make the saw edge stand out.
With a deep saw blade, like the one I am using, the blade will continue going straight on once the cut gets deeper.
To make a cut at a constant distance from the edge of a part, I sometimes fix a loose saw blade to my bench.
To raise a saw blade to the proper height I make a stable stack out of wooden popsicle sticks and cardstock, put another popsicle stick on top of the blade and clamp the lot down with speed clamps.
Then I stand the part on its edge and gently move it along the saw blade, this works well for shallow cuts.
Moving the part along a fixed saw blade does result in saw dust scattering around all over the bench.