How to tell if I have a carbide tipped blade

Back in the day when I used to put up vinyl siding, I found that the best way to cut it with a circular saw was with a cheap 140 tooth plywood blade installed backwards (to give the teeth a negative rake and prevent chipping):

For really hard plastics, I've used a diamond abrasive blade before and that did a great job (these are incredibly expensive if we're talking about a single cut though). I would imagine an abrasive blade for cutting metal would do just as well though:

You should be able to pick up either of these for less than $5.

Wear good safety glasses and do a trial cut first with whatever option you go with - plastic will chip long before it will bind the blade in most cases, and these can be both sharp and high velocity.

The diameter is important, as that's the maximum size blade that will physically fit in the saw. The arbor size is important, because that's the size hole that will fit on the saws mandrel. If either of these sizes are wrong, the blade simply will not fit on the saw.

The thickness of the blade doesn't typically matter, as far as fitting on the machine. Unless you're talking about a dado stack, but you'd not be putting that on a miter saw anyway. The blade thickness, or kerf, only tells you how much material will be removed when cutting.

The number of teeth influences the speed of the cut, as well as the smoothness of the cut. Generally, more teeth give a smoother cut.