When I do servo sizing and I am not concerned about being absolutely sure that I am getting the smallest possible size, I do this:
1: Calculate max force for peak loads
2: Calculate max force that is sustained
The possible forces are usually these:
1: Force to accelerate the axis
2: Cutting forces
3: Friction forces
4: Gravity forces
In a CNC machine, the forces from cutting are the biggest, and they are sustained. This is true for machines with lots of power, but not true for all small machines, say one that uses a 1mm ball end mill. Here is a link that discusses cutting forces:
Also, here is a discussion of ball screw rotary to linear force discussion.
Also, you will want to add your friction of your ways at max speed. This may not be trivial if you are not using linear bearings.
On top of this, you probably want to oversize 20% because motors have tolerance on their torque constant (10% roughly) and another 10% just because it makes me feel more comfortable
From this, you can calculate the torque required and buy a motor that is appropriate.
Hope this helps and inspires someone else to add in...