I have an old house as well with a bathroom similar to yours before I renovated it.
To
answer your question, I just try and use as much naive lumber as possible and stay away from plywood if I can. I do have a sawmill but I think even buying your own real lumber
wood in natural building. For me, it kind of helps that I literally live right across the road from one major sawmill, and just 5 miles up the road is another. I think between the two they employ about 400 workers. So I know when I buy hardwood or sawmill boards, I am keeping my neighbors employed and the wood is locally sourced and produced. It is not so much that way with plywood.
As for the renovations itself, I try and stay period specific. I live in a Victorian Home and despite a lot of extra work and cost, I try and maintain the Victorian Era look.
When I renovated my bathroom it was oddly missing a door on the
linen closet, but my neighbor (a antique shop) had an old stained glass door. I could have bought a new door from Home Depot for half the cost but instead I fixed the rot, replaced stained glass panes, and in the end spent $200 on an old door, but it looks like it was forever in this house.
And in the end, it has been good. I have added a new skill I never had before. Stained Glass work. I can now cut, shape, and install stained glass which is incredibly useful renovating an old Victorian Home. From
lights to kitchen cabinets, to bathrooms and windows; stained glass proliferates this old house.
PS: That sawmill right across the river from us? Despite being a 24/7 operation, we have got so used to the sound of the sawdust blowers; of that constant "hummmmmmmm" that when they shut down on holidays, we have a hard time sleeping. We are just so used to it, like an old friend.