CNC Machine for relatively precise wood carving-what would I need?

Hi,

First of all, let me say that I'm relatively new to this.

I'm trying to build a machine for wood carving. It would have to be
able to cut with enough precision to cut an approximate 1mm groove.
It would also have to be able to cut 3-dimensionally. What would I
need? What would it cost? What would I need in terms of computer
controls? Price isn't much of a problem, so I'm open to any
suggestions. The work area would have to be about 22" x 16" x 1".

Thanks for your time.