How big the chuck on the MIll/Lathe head you aim at? That will be very important at deciding on all elements.

I was thinking at one time to do this and went to the conclusion that cheapest will be to fit a mini lathe driven by 700w servo with brake if doing small parts. And use 200mm chuck and design everything from scratch if need is for bigger parts. Copy/ paste then the build that was mentioned before as its well documented on forums and videos