Wood will function better than clay in relation to temp and moisture swings, provided you accounted for that in the beginning.

The best thing to do is the allow the planking to do what it wants to. don't force it to do what you want it to, it will win. That's why you put the boards in channels, so they are free to move up and down and side to side if they want. And they do want to. That's also why you use narrow boards. I am thinking 1x4 for anything expected to support plastering, just to resist cracking.

One thing that you can easily do to prevent the ingress of moisture from the inside is to use an old technique, seal the cavity-side face of the inner planking with tar or some other sticky water proofer. But do not DO NOT use a vapor barrier as this will just hold the moisture against the wood, which is BAD.

The inner planking is no different than using boarding on an interior wall. The outer planking is essentially the same as plywood sheathing. The benefits of clay are not to be underestimated either.

The wood species used can just be common pine. Or it could be cedar. I would be afraid of using hardwood in most cases because of cost and stability.

If you are still scared of moisture travel, plaster the inside with clay. That will stop it right then and there.