** spellcheck mishap: I meant Board&Battan NOT Batman! lol

Gorgeous woodwork! It looks to be in good condition so my advice is live with it as it for the current time. Definitely do not paint that trim as the original details are part of the value of the property. Some features should not be updated!

I like it. Scrub it up good and live in it with
your things in place before you decide and do something you can't undo. I would be worried if stained too dark, it may lose any wood grain visual interest, and just darken the house.

I would not recommend doing anything with that woodwork until you have had some time in the house. Old house woodwork is a labor of love as if you even value your own time at minimum wage, you will have a huge investment for only a small gain in market value.

I added crown molding to my 1933 Tudor and all my visitors comment on the original woodwork and are just amazed that the crown is new. If I added up the hours I worked on that project, it probably works out about 1 hour per linear foot. Then add the money for all the materials with different types of shellac flakes, solvents, dyes, stains, finishes and abrasives. The unfinished maple crown was the only bargain in that deal!

If you want to try working on some woodwork, consider tackling the stairs as that will be enough of a project to absorb lots of time and energy. The wide trim on the left side appears to have knots that make me question whether it is original as finish trim of that era usually was a consistent grain without knots. Plus, that oak newel post doesn't match up either, although it might match the treads.

Don't take on too much at first as it is easy to get too deep into a project before you realize how much you don't know and find other projects calling for your attention