With only 1200mm travel required, you should be able to use a ballscrew under 1500mm (perhaps 1300mm), in which case RM1610 would be fine. Bear in mind that the torque required to accelerate the ballscrew goes up with the diameter raised to the power 4, so increasing from a 16mm screw to 20mm requires 2.44 times more torque from the motor to accelerate the screw. The ratio isn't quite so bad when you factor in the inertia of the gantry, but it's still significant and best avoided.

You've currently got the top Y-axis rail longer than the bottom one. If you go down that route, then you can increase the spacing of the bearing blocks on that rail (a bit) without compromising travel.

Your requirements for this machine aren't remotely ambitious, so you'd be fine with 15mm rails all round, but it can make the design easier, particularly on the Z-axis, if you use 20mm rails. Just draw it and see what you come up with.