The best blade is a table saw with a carbide tooth blade with lots of teeth. Of course, that will only work for straight cuts. For curves you can use a jig saw with a blade that produces a kerf (not a hollow ground blade) so that the sides of the blade don't rub across the plexiglass and cause heat. The reason for cracking is vibration - the plastic needs to be firmly supported.
I've had good luck cutting curves using a router with a template. Use a small diameter (~1/4") straight edge carbide bit, and go slow.
Once it is cut, use a file or sander to smooth the edges. Professional shops will polish the edges using a muslin wheel charged with rubbing compound. The trick with the muslin wheel is to get the edge hot enough to melt a bit and get smoothed out, but not burn. It takes a few tries to get the hang of it. At home, I've had good success with sandpaper, going through 80 - 100 - 150 - 220 grits, and then using a propane torch to flash the edges. Again, you must balance between heating it enough to polish the edges and burning the edges. Practice on scraps.