You're in a quite moderate climate so insulation is a waste of time and effort -- creating a hotel for rodents while offering no benefit to the chickens. 
My open air coop https://www.backyardchickens.com/threads/large-open-air-coop-in-central-nc.1443812/ is a big wire box with a 3-sided shelter at one end. For that shelter I used fence boards, but shiplap could have been an option over the wire.
The important thing is that the wall material be strong enough that a predator can't break through it.
This is a bad idea.
It's the nature of chickens to scratch and dig so putting hardware cloth on the ground both frustrates their instincts and hurts their feet. It's better to use an anti-dig apron around the outside.
@aart has a good example of how to install one.
I don't think you said how many chickens you have or how big a coop you were planning?
Here's some general information for you about that:
The Usual Guidelines
For each adult, standard-sized hen you need:

I do know that every inch of my coop will be protected with hardware cloth.
My open air coop https://www.backyardchickens.com/threads/large-open-air-coop-in-central-nc.1443812/ is a big wire box with a 3-sided shelter at one end. For that shelter I used fence boards, but shiplap could have been an option over the wire.
The important thing is that the wall material be strong enough that a predator can't break through it.
I’m using the hardware cloth under the floor of the coop too.
This is a bad idea.
It's the nature of chickens to scratch and dig so putting hardware cloth on the ground both frustrates their instincts and hurts their feet. It's better to use an anti-dig apron around the outside.
@aart has a good example of how to install one.
I don't think you said how many chickens you have or how big a coop you were planning?
Here's some general information for you about that:
The Usual Guidelines
For each adult, standard-sized hen you need:
- 4 square feet in the coop (.37 square meters)
- 10 square feet in the run (.93 square meters),
- 1 linear foot of roost (.3 meters),
- 1/4 of a nest box,
- And 1 square foot (.09 square meters) of permanent, 24/7/365 ventilation, preferably located over the birds' heads when they're sitting on the roost.