You're not looking at high forces and backlash shouldn't be a problem as you're cutting in one direction so no need for a ballscrew. I think you're looking at a plain acme / trapezoid leadscrew with maybe a delrin nut. You'll want the leadscrew to be good quality so it moves smoothly and the guides for the cutting head should be quite heavy duty - maybe think about further damping the movement by using dovetail slides covered with a thick oil (I believe there are oils that are particularly sticky for that kind of application).

Good picture of a lathe on Wikipedia...