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Shiplap apparently isn’t a “cheap” finish.
Most likely not doing the whole interior in it.
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No, not cheap at all.
I've seen some attempts to do it more cheaply, with some type of laminated wood (thinner plywood, etc) but I'm not sure it saves much, if anything. (this is "shiplap look" not actual shiplap....in other words, there is no dado cut to overlap. It's just stacked boards, which is how an awful lot of interior shiplap is done. It's not real shiplap.
I've seen it done with pallet lumber, which would be a pita but can look really cool. Not sure if I could give up a set of knives on a planer to get it smooth.
I love using old, used lumber. The floors in half my house were once an old barn. Made a lot of mistakes, learned a lot, would do it WAY differently. But still not sure I'd a-pay the cost of having that planed by a pro. (We did it ourselves.) or b-give up a set of knives for it. We used a floor sander to take down the unevenness (one of the square ones that will get into the corners. I would not risk destroying a drum on a rental drum sander.)
ETA: The floor is not meant to be a jack. Just...using anything except prepped lumber ends up taking time and (sometimes) money of a different sort/direction.
There's not much way around the cost nowadays, even if you have a free source of lumber, unless it's perfect when it gets to you.
ETA2: Even if you were inclined to use some kind of pressed/particle board (which I would not guess you are, just observing the quality of things you have posted) it takes too many coats of paint/primer to hide the substrate, IMO, and...just...putting that on the walls...yeahhhh I just.....no.)