I'm just as in love with shiplap as you are... I have it in my new kitchen renovation and have used it on client projects. In each application, there have been some small decisions that have made a big difference, and I wanted to share some of those here.
Shiplap used to be an inexpensive wall covering that was often covered up with drywall... now, it's the star! For decorative applications, the boards are installed (using finishing nails) over finished drywall. The size of the boards can vary, depending on the application and desired look. I wish there was a pat answer that applies to every house, but I don't find that to be the case. Here is a 6" board and below a 8" board. I think they are both perfect in their spaces!
The material itself is the most common question... but here, I again find there is not just one answer. The material depends on the application.
In my kitchen renovation, we used ship lap on all of the walls, including my backsplash. Because the boards were going to be near open flame and wet surfaces, we used smooth cement board (the same material used as siding on exteriors). My splash is waterproof, washable and non-conbustable. (genius!)
This wall is a combination of both MDF and cement board... and it's undetectable. We used mdf on the entire wall, then switched to the non-combustable cement board for the fireplace surround. The size of the planks is the same as is the paint... perfect solution!
For a wall or ceiling installation when those elements aren't necessary, we often use mdf. It's inexpensive, easy to install, sand, and paint.
Another option is true shiplap with has a rabbet edge (similar to tongue and groove). Each board overlaps, but a gap is visible. Traditional boards are shown here on a barrel ceiling. (above image)
Spacing is another factor in proper installation. Cement board and mdf have flat edges, so they require a space to create the gap between each board. I like a visible shadow line, but not a gap so large that dust can collect... my go-to is 2mm tile spacers, but a nickel will do in a pinch!
For my kitchen, the painters brushed the oil paint on the cement board... they are professionals, and therefor there are very few brushstrokes. On new construction or larger renovations, I prefer the paint to be sprayed on for a flawless finish.
Corners can be tricky... the edges where all of the boards meet needs to be clean. The installer can choose to miter the corners to create a sharp edge, or butt joint them and then choose which side has an exposed (but clean) edge.
I hope this helps you navigate your way through one of my favorite building materials... I would love to see how you are inspired by shiplap!!