How do I determine the spot size and focal length of my setup?

For a point source, near collimation can be assumed, so the beam will be the “clear” aperture of the lens. If a fiber is attached to the lens, the divergence angle can be calculated depending on the height of the fiber. This information allows you to calculate the spot size at a distance.

Tan(Theta) = (Height of fiber)/(Focal Length)

Focal Length = Height of fiber = (1/2)*core diameter

Theta = divergence angle