I agree with Briar that the poly is way tougher, but acrylic is harder to scratch. Poly will flex quite a bit, acrylic will not flex much before it breaks. The tougher poly is easier to work with.
I have used a circular saw to cut it as well, the secret is a brand new carbide blade. A router is the best way I have found for complicated shapes, but again the bit must be new and perfect. With the router you want to feed the material pretty aggressively, or you will be rubbing the material with the bit and it will melt. If it melts the game is over, so keep the bit cool with fresh material to cut. You can use a round-over type bit to clean the edge up, or you can just sand the sharp edge off. The easy and best way to finish the edge is with a router, just feed it aggressively. Drill all inside corners that are not routed to a radius to keep them round, a radius is necessary to prevent breakage. I would suggest that you lay out your project and practice with the waste material to get a feel for it before tackling the meat of the job. It does take a bit of feel to do it without breaking it.
If the project you have in mind can be opaque Delrin is 100 times easier to work with and more durable yet.
The big chain in the upper midwest is Cadillac Plastics, I think there is one near you Doc. You can order from them over the web too. Hope this helps.