I want to change from R&P to ball screw on my gantry

[MrRo]

I've got a half built machine. The overall plan was to pretty much clone an Avid style one.
I have used a fairly standard chinese gearbox on the Y had some plates cut and have something that should work. Though not very elegant

Picture appears to be upside down don't know why.

I've decided that i'd be better off using a ballscrew on the X from the forum a pitch of 10 seems to be recommended.
The beam is1850mm wide though i'm only concerned with being able to have a working area 1200mm wide but bigger the better.
Reading the forum I think it's best to have a 3:1 ratio belt reduction?
What diameter ballscrew should I be going for?
I've got 12Nm closed loop steppers, probably over the top



I have very limited workshop facilities, so can I get this going with as many off the shelf parts as possible?
Any suggestions welcome.



Thanks