Why not get a bit of manual lathe experience before CNC?
While a CNC mill is capable of making shapes that a manual cannot easily do, the same is not true of a lathe. You can make most shapes (except complex organic curves) with the compound, taper attachment, and form tools without sacrificing the basic functionality of the machine.
Once a machine is CNC, it is significantly less useful as a manual machine. I started in CNC when I was 16, converted both my mills. 10 years later I find myself really wanting some manual machines.
If you need to make hundreds of the exact same part, or have super complex geometry, then CNC is a good idea. After 5 years of lathe ownership, I still have no interest in making it CNC.
With all that being said, if that is really what you want to do, I have done 8-9 CNC conversions and can definitely help you pick out hardware. It is expensive though, even if you try to do it cheaply.