There is no question that proper ball screw & nut will be far more accurate than anything else.
But, if it is a thin (eg 10 mm) ball screw you may (will) have problems at speed. It will flap around at times something awful.
You can solve this by going to a more solid ball screw - say 40+ mm. This will however be more expensive.
However, the funny thing I have noticed is that once you are running in production mode, the original cost seems to just disappear.
Single screw vs double screw: your call. A really solid carriage and a really solid single screw would work fine, but it would need to be Really Solid. You could get this with heavy linear bearings. Mach3 can handle double screws just fine.
Cheers
Roger