Ballscrew design and 12vdc rpm and torque calculations help required

[rjsutton]

Hello
IM normally quiet smart but the following has me stumped. My Carpentry brain just cant work it out
I have a machine that has a 200x 20mm sliding plate ( slides on 2 SGB20N bearings each end) it has a vertical load of 400N each side
I need to get this plate to slide(powered) from one end of the rail to the other (900MM)
I think maybe a 16mm Ballscrew driven by a 12vdc ( it is to fit inside a car ) reduction right angle worm drive gearbox (3000rmp 30 watt motor)
if this has and encoder i could set the limits . it must travel both ways)
the overall speed of the plate is 0.045m/sec ( 20 secs to travel the 900mm so its not fast)
im not sure what type of ballscrew 1604-1605-1610 ? would be best ( question 1)
then i need to know the output rpm of the gearbox and the torque required to move the plate easily ( question 2)
a suitable model no of motor-encoder-and gearbox ( Question 3)
Im not even sure IF this type of system will actually work. I thought of a rack and pinion setup but i dont have the space or know how for this either.
The ballscrew would be mounted on the side wall of the machine with standard BF/BK bearings and the Ball nut and housing secured down to the top of the plate.
Ive googled and found a million calculations but i just cant work this out
Any help hugely appreciated. If thi