I just use an ordinary woodcutting blade for acrylic, it doesn't melt the acrylic as long as the backing plastic is still on. Whenever I have made cuts without the backing plastic, the acrylic has melted on the cut. Not sure why, but it's happened every time I have used acrylic.
Whenever I am cutting anything, I always undercut by 1-2mm so I can file down and get a good finish. I never try to cut exactly to the required measurement because if I go wrong, there is no margin for error.
It's always wise to get some scrap in the material you are going to be using, and practicing cutting, especially if you aren't confident with the tools.