Ok got to be careful here don't want to sound 2 faced after the ranting but I agree with Mitchejc that the base needs to be strong and sound just like any well engineered structure the foundations are important.

Now this doesn't mean going bonkers but I'm afraid it does mean much more than you have drawn there. I'm not getting into the Steel/aluminium is better than wood argument because you clearly have your sights set on using wood so go for it.! . . But I'm afraid you'll need much more structrue than what you have there.!

The other things I see are classic under estimations of forces acting on parts of a CNC machine. Like the gantry sides are too flimsy for there height and when in use they will flex and resonate when short fast back n forth moves are happening while cutting. Just try shaking 20Kg back n forth really really fast to see how it feels and the effect it has on your arms.?

Single or twin screws depends on what your cutting but your border line on the width for using 2 screws. If your planning on cutting harder material with any intent of decent depths then you'll want twin screws.
If you stick with single then make the lower spanning brace much wider to help combat racking.

Z axis design is bad news and will be a proper bitch to setup. Why re-invent the wheel just use the proven concept of rails on front plate bearings on rear it works perfectly and is easy.
Y axis screw is way too high for my liking and you want to try getting it lower if possible.


Other things with design to think about is how your going to build it and allow for adjustment etc for setting up.! I don't see much.?
Also don't forget cable runs etc.