Your space is lovely. You do not need to purchase it all at once. It will evolve as you find things that you really like.

Framed or canvas may well depend on the style of art you like.

You really have a lot of options that would look good on those walls. It will depend on the art that appeals to you and the mood you want for your home.

Can you explain what we're seeing with the reflections in the 2nd and 4th pics? It looks like something is mirrored, but I can't seem to understand what it is.

I don't think there is one perfect solution to your problem. I could see one big piece on some of those walls, framed or unframed; or a set of same-size, same-framed items on a common theme; or a full-on gallery wall.

I agree that it is more fun to find items that you like over time rather than run out and buy something just to fill the space. And you'll probably be happier with it in the long run.

If you get a bunch of different items, framing them all the same way can be a way to tie them all together (though that isn't a must). Stretched canvases don't need to be framed if the edges are painted, which can save money (framing can be expensive). Most of my canvases are unframed, but I framed a few because they look better that way. Off-the-shelf frames are available in certain standard sized. If you are lucky enough to get artwork in those sizes (canvases come in more sizes, but certain dimensions are fairly common), it is pretty easy to frame your own, as long as you are happy with the limited frame color selections off-the-shelf.

The hallway is...a hallway, that is to say it has a limited width. So while putting a very large piece of art may suit the wall size, it would be very hard to view properly? I realize not all art is for viewing, its decorative too, but that could be an awkward aspect. Though, on the other hand, if (for example) there were a series of posters (which come in all sizes) from perhaps places you had visited, or would like to visit ...those could make a nice series and be of a size that could be appreciated within the viewing width of the hall. Although, then I wonder how that type of arrangement would relate to the rectangles of the wainscoting (not sure what that trim is called). So a bunch of aspects to consider. I think the suggestions to find art that resonates with you is great.

I agree that with a narrow hallway like that, it is difficult to view art from a proper perspective. Therefore, it might be good to use something sculptural, such as masks, if those appeal to you. I have a collection of African tribal masks and Mexican masks that would work in that sort of space, but that might not be your taste. You could also consider a tapestry or maybe even some macramé, which is not something I would ordinarily suggest, but it does have a three dimensional aspect to it. Since you mainly just walk through a hallway, I think it is best to put something there that will be interesting to view in passing and that will look good from a multiple of angles. A mirror might work on one of the walls (to increase the visual space), but it appears that that would cause a problem with the light.

If I put masks there, I would put them on one wall and a tapestry on the opposite wall. The tapestry could be a textile that relates to the masks.

It looks like your floors are not yet finished. I would give myself plenty of time to think about it.

Maybe just a grouping of black and white photographs or even a grouping of soft muted pretty framed prints? No perspective needed for these.

Photography is a good choice, especially B&W, if you have that.

With your beautiful wainscoting, I don't think you need much on your walls.

Although the hallway may be too narrow to view larger art pieces properly, smaller paintings or photographs can still work with the amount of space you have. I would arrange 3 pieces along each wall and have them centered at equal height.