Adding ball screw to lathe for Electronic Lead Screw

Greets to all!

I am outfitting my Sieg C4/LMS 3536 9"x16" lathe with an electronic lead screw control. I'd like to add ball screws, but don't want to break the bank! Probably the existing 20mm x 2mm standard LS is fine but want to change to ball for other reasons,
How much does the diameter of the ball screw matter? Can I go with a smaller diameter for lower cost? Also would like to get pointed to info on pitch. Length will be around 900mm.

Tks!

=Alan R.