Lots of specialized terminology so far. Rake is pretty important. Here is a diagram that explains rake. I have cut this stuff on my table saw (table saw zero clearance inserts), and it is pretty messy. Just don't let it linger on the blade, keep it moving forward into the blade, but don't push it too hard. Haven't used a router on it, but if I were going to, I'd use an up spiral bit. This bit is ground so it lifts the chips up and out of the cut. Other types of bits might quickly wind up with the plastic melted onto the flutes (cutting edges) and be all but impossible to remove. Same would apply to a saw blade. The negative rake is something you have to double check on any blade you are considering. It is not always obvious just looking at it.
More teeth on an 8 inch saw blade makes for a smoother cut. At any given speed, more blades will mean smaller spaces between each tooth's cut, thus smother. The illustration also reveals the difference between crosscut (across the grain) vs. rip (with the grain). The large gaps (gullets) between the rip blade's teeth, let it carry off very large amounts of sawdust or waste. Crosscuts produce less sawdust per inch.
Tooth shape matters. Flat top teeth make for a flat bottom groove when you don't cut all the way through. This is very useful if you are cutting a groove in your workpiece into which something will be fitted. The smooth bottom makes for a stronger glue joint. But if you're using it for a through cut, the raked, or top at an angle tooth makes for a very clean slice through the wood or other material. Through cut just means cutting all the way through a piece (cutting it shorter for example).
I've also attached a short pdf on saw blades that lays out the big facts on sawblades.
Hope this is helpful. There were a lot of tech terms flying around the responses.
The more I do, the less I accomplish.