10x Objectives Comparison

You're correct, the critical direction is vertical, assuming the camera is looking straight down on the coin. The stack is created by varying the distance between camera/lens and coin.

As long as you are not planning to go to higher magnification than 10x, I see no reason to go with a stripped-down microscope stand. The main reason to use one is to get higher vertical resolution, but even at 10x you generally don't need better than 10um resolution, and this can be achieved with the smaller and cheaper Z-stage I linked to. Plus, it requires no modifications be made!

But if you do go the stand route, make sure you get one that has the correct adjustments. You are looking for a stand that has concentric coarse/fine adjustment knobs. These have "infinite" fine step capability, ie you can turn the fine focus knob forever and it will keep moving the stage. Some don't have fine focus at all, while others have limited range to the fine focus. I don't think the Leitz stands you linked to have this infinite capability, but I may be wrong. Not my area of expertise.

You usually only use XY adjustments to frame the shot, so precise measurement is not needed. I suppose if you do stitching then it's important to have reasonable XY measurements but even then you can probably do it visually since you will almost certainly ensure some degree of overlap.