Stay away from particle board at all costs. It's far less durable than MDF. Melamine isn't all that hot either, as it is very similar to particle board inside. But it does have a nice pre-made finish.
I wouldn't use plywood unless you plan on laminating it, or you spend the extra for hardwood laminated or MDO. Otherwise it'll just be ugly.
MDF was engineered for low cost cabinetry with all the desireable properties that go with that application. In other words, it was designed for what you want to do with it

. How well your project comes out with MDF (or any material for that matter) will depend on whether your construction methods are compatible with the material.
There are lots of different pieces of hardware that are specially designed for this type of material. If you choose to take shortcuts or use hardware designed for other purposes, the quality of your project will probably suffer as a result. Most of the time, the individuals that give MDF a bad rap never really gave it a proper chance. A little research goes a long way.
RandyT