You're going to struggle to get good feedrates with only 3mm pitch screws especially on the X axis where whipping is likely to be a problem over that length. You'll need good, probably one angular contact pair, bearings at both ends of the screw unless you tension the screw, or rotate the nut instead of the screw. I did the latter on my 1.7m X axis, 20mm diameter screws.

I also think you will have to put wires under the gantry (like on the old drawing drawing boards) to stop it racking. It would be better and easier to just use 2 screws though.

Difficult to say about motors without knowing more (mass of gantry, desired feedrates etc), but as a rough guide 3nm nema 23 for Z and Y, and something bigger (34 size) for X iff you've only got one screw.

You say not fast, but do you really want to have to wait a few minutes for the gantry to traverse the length of the bed? That may well be the case if the whipping on the X axis screws is bad.