I like that you started your post with you're lucky enough to build a brand new shop. Great outlook and I envy you with your project. There are two ways to answer your question about what to use so I will share my thoughts:
1) if you want to use 6-12" wide boards, and they are not well seasoned, you could have 1/4-1/2" shrinkage. Yes, a shiplap would help conceal the back of the openings and if you choose to do that, the easiest way to do it is with a router and a rabbiting bit. Clamp down the board and run your router down the edge. That way you'r not having to manage an long board on a router table, or table saw if you use a dado stack.
2) there are 2 ways to look at the walls in your shop. If you want them to look nice (more like a house), you could use drywall or decorative panelling sheets. If you want them to function as storage, I suggest using wood so you can easily mount things to the wall.
I've chosen to make my shop look nice and functional as well. My solution is to use a white brick design paneling for the lower portion of the wall as it looks nice and it's a light color. The upper portion of the wall is 3/4" maple plywood. On the plywood I've hung french cleats across the wall which allows me to hang tools, shelves, jigs, etc. in a way that's flexible to change as my tool/jig collection changes over time.
This was a little long, but I hope it helps. Let me know if you have questions or want some photos.
Scott Bennett - Sharing the enjoyment of woodworking via Woodshop Therapy.