You can cut it with with pretty much anything. During my project I used a table saw, skil saw, jig saw and router, doing different cuts on the MDF. Use a table saw where you can for the straightest cuts.
If you are going to build the whole cabinet out of MDF I would look for the "lightweight" MDF, it costs a bit more, but weighs less, and when you use 2 1/2 sheets for your cabinet, it gets pretty heavy.