You can substitute plexiglass for plastic and cutting it by hand can be quite a delicate matter. One way to cut circles into plexiglass by hand is using a hole saw. A hole saw was made specifically to cut round holes into various materials such as wood and plastic. It can also easily work its way through plexiglass. Another way to cut a circle is using a jigsaw. Jigsaws have thin blades that penetrate the material, making it possible for them to make small turns while cutting. All you need is a good grip, some patience and a steady hand to be able to successfully cut circles into your plexiglass.
Remember to look up a few safety and instruction videos before you use either of these tools for the first time. Don't forget to always put on a pair of gloves and safety glasses before you start working.