Hi,
you will need a machine that is stiff enough to contain cutting forces without deflection or it will screw the accuracy and finish of your parts.
You may rather imagine that you can use a low power spindle, and you may be right, but I think you'll want at least 2kW. At 2kW you should be able to use single
phase power, with a decent high current outlet. I say this because you'll need a tool about 1/2 inch in diameter otherwise it will deflect, remembering that it will have
to cut two inches deep. That tool will have considerable cutting forces and therefore a stiff or rigid machine will be required.
I would suggest that you keep the gantry fairly short say two- three feet. It so much easier to make something stiff if its small. That would mean that you would
lay the timber long ways. The gantry would then traverse the length of the timber. Rotating ballscrews over that length is not practical, they would have to be large and therefore
expensive. I would suggest that you need rack and pinion, at least for the long axis. The gantry and Z axis could be much shorter and ballscrews would be a good solution there.
What sort of budget do you have in mind? That will determine what you can door indeed if it can be done at all for a given sum.
Craig