Without doubt if you want high tolerences then you need to go with a Fixed gantry. Better still use a design that doesn't use your typical Z axis approach.?
To get the best surface finish and hold tight tolerences it's critical that tool length is controlled and kept to minimum. Typical Z axis is always a compromise between material clearence and tool extension.
A far better way is to not have a Z axis as such but rather have the Axis which spindle runs across raise and lower. This ensures the tool extension is always the minimum it can be regardless of material height. The only extension is the tool stickout from the spindle. This results in much less chatter, less vibration and higher tolerences.
Check this out to see what I mean just make a better job of it and use a proper spindle.!!. . .


Make it very strong and Dense to minimise vibrations.

Wouldn't even think to use round linear rail if you want high tolerences as it will be the worst thing you could do and you will regret it for the slight difference in price.
Building a machine to hold tight tolerences is very very hard to do and will require substancial effort so don't spoil it for sake of few quid extra.