Rip out the layers of linoleum and put the same wood as in the rest of the house

Match if possible.

Thanks for your responses! Does that mean that you think even if it's not perfect, matching wood type and stain as best as possible is preferable to a contrast? I don't have any experience with this, but it does seem like it would be quite difficult to match brand new wood and stain with a seasoned floor from over 70 years ago...

Hi---I recommend going with a tile instead of wood because there are differences in floor levels---having an entirely different material will make for a better transition. Delighted for you for taking out the wall-it's a Huge difference. Hope this is helpful. Good Luck!
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Caitlin, I would be very surprised if the original floor is pine and not oak. Consult a wood floor professional. It should be easy (though not cheap) to blend the two floors though you may need to refinish the original wood. In my experience, if you want wood flooring, you will never be happy with anything else.

Hi! From the picture you've provided your original floor does appear to be southern yellow pine. Fortunately, you will be able to match the old color/patina of your existing floor by using a reclaimed long leaf southern yellow pine. Just match up the widths of your existing floor boards to the "new" boards, as well as the lengths. (you don't want short, choppy little pieces).

Next, lay the reclaimed boards in the same direction as the original floor. Sand the original floor to bare wood, then apply a finish to both floors and I am confidant you'll be amazed at how well the two floors blend as one.
Here's an example of a reclaimed long leaf southern yellow pine floor I made:

You can also have the reclaimed pine graded to include more, or less, character to better match your existing floor.

As for the 1/4" difference in height in the kitchen, is it possible to tear out any of the existing subfloor in there? (I'm assuming the linoleum is already taken out and you're still 1/4" higher?) If not, then yes, a transition piece can be used and will look fine.

Hope this helps!

Yes, it's definitely pine. Thanks for this. Unfortunately the subfloor is rotten so it would be a much bigger, more expensive job to get rid of the height difference. I'm going to start looking for salvaged wood from the same era - fingers crossed!

We have reclaimed heart pine flooring here: www.barnstormersreclaimed.com
There are a few other reputable companies that specialize in salvaged heart pine flooring as well. Goodwyn Pine, Carlisle Wide Plank Flooring and Long Leaf Lumber.

Thanks so much - I'm passing this all along to my carpenter.