Depends on how great you want the results to be and what you're willing to spend.
For the work, machining soft plastic to relatively low precision, most any CNC Router you can get working that has a sufficient workspace should do the job reasonably well. May not be the prettiest results, but could definitely get you in a good ballpark for hand finishing if you plan it right.
If you plan to do a lot of CNC work and want to move to other materials eventually, you'll probably have better luck finding a machining forum and looking through the threads they no doubt already have discussing at great length why machine X is vastly superior to machine Q in every respect.