Don't stress yourself, just make a bathroom that works for you and is easy to maintain.

A "nod" to the era is sufficient.

If you match the dark grey tiles to the grout in the shower, it could look good. If you found a grey slate-look tile it would even look reasonably "period".

Another vintage look would be hex tiles, in white or light grey with darker grey grout.

Have you looked at images on Houzz.com? There are so many pictures. You can search for gray floors. Hanging sinks. What ever. What about a nice hybrid of vintage and modern? Not to tire people of my bathroom remodel but I have a picture of my almost finished slate tile floor. Be aware that there are floor stiffness requirements for tile and even stiffer requirements for stone. If You don't have access to improve your joist and subfloor to meet the demands of ceramic or stone, there are some lovely floor coverings that look like stone.

My "in progress" slate floor. This is 6x12 Brazilian slate that I cut down from 12x12 tiles (the white tile boards are my wall sample boards, testing grout colors):
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I've attached a link to a recent bathroom remodel by Barbcollins. She used a vinyl product for her floor and there is a picture of it on the post. I think it is very nice looking.

Here is a link that might be useful: Barb,s Budget Bathroom

I love that slate floor! If we go with dark grey that's the kind of look I have in mind. Hex tiles are another thing I have been googling. I really like the look. But I am concerned that the grout lines would be difficult to keep clean.

I wonder about sheet linoleum? The real stuff, rather than vinyl. Seems like it would be easy to keep clean. It was used in kitchens in that era, but I don't know about bathrooms?

Houzz is such a great source. I have been searching all sorts of combinations on there. It really cemented my idea to go with grey floors and white subway tiles, plus beadboard.

Thank you!

Have you considered marble basketweave? We have polished marble basketweave in our 1950's era house and it adds a vintage touch. The grout is light gray and if properly sealed, cleaning is not a problem.

Light to medium grey grout is easier to keep looking clean.

I had an 1880s house that had one of the original hex tile rust and cream bathroom floors and they were in good condition. Pity they were split between two apartments in the 1920s and ended up in closets.

This is the grey I'm using. It's ceramic and very reasonable. the rest will be white with marble accents.

Phylhl, Very pretty!

Pip dog, lovely basket weave! And phylhl, that's a really nice use of tile!

Thank you all!

crl - I put Marmoleum sheet flooring in my previous house's master bath, and loved it. The texture underfoot is really nice. But I also like the basketweave and hex floors for a vintage style bath. My husband nixed that idea because of maintenance concerns, so we went with a honed faux-marble 12x12 tile with gray grout in the current project. I think it will look good with our old house because it's very neutral but slightly elegant and formal.