Post photos, please.

photos added showing two of three entrances (third side is same as light oak entrance), the current vinyl, the one we currently like, and the dark blue cabinet. The lighting might not be ideal, but hopefully is good enough.

Don't get white or very light close to white. I was so close to buying something similar to your choice until someone told me that they had gotten light close to white vinyl flooring and it got a yellow staining in the walking paths and when they complained there was fine print and this was not covered

I asked at the flooring store and they acted like they had never heard of such a thing. I called the manufacturer and they acted pretty much the same. Then I looked stuff up on the internet and called the manufacturer back and pushed about staining caused by asphalt being brought in on the bottom of your shoes from your driveway. Bingo - will permanently stain flooring and "Environmental Staining" is not covered.

Shaw's Warning about Vinyl Discoloration Due to Tar or Asphalt

Yellow discolorations develop slowly by the transfer of trace amounts of asphalt residue through the accumulation of thousands of footsteps.
"Antioxidants used in the manufacture of rubber and petroleum from exterior asphalt sealants and/or spills tracked in on shoes and casters may cause permanent discoloration to any resilient floor. The stain gradually appears over time." ---Armstrong

Warranty limits can be revealing, as in the case of Mohawk's Master Resilient Warranty:
Exclusions: "Discoloration from underlayment panels, mold or mildew, rubber backed mats, asphalt or deicer tracking."

Other flooring manufacturers warn of the same risk of yellow discolorations caused by tar, asphalt, or petroleum byproducts.

I've not noticed that problem with our current old vinyl flooring, but it is old and pale yellow so maybe that's why. I never knew asphalt will stain vinyl. Thank you for the tip.

I’d go with anything but wood or a wood look alike.

Any chance you can sand and re-stain those old floors because they are to die for.

I would love to refinish the old oak floors but they are badly stained, water damaged and creak a lot in spots. So I wonder if they are repairable. Alas, that will come later anyway, as the cost of dealing with that floor is too high for us at the moment. So next step is the kitchen floor.

We're now wondering if we should go with an oak / honey oak look in the kitchen, and possibly repaint the cabinets white/whitish.

The tiny pictures don’t really offer enough to make a suggestion that will go with the whole look of your home ...under the present situation you described i would seek out a low end temporary solution....maybe a pattern... that has both of the wood floor colors...to tie them together for now ....and to be replaced when you decide what to do with the pretty old floors...in the future....

Another option would be a pattern with white and blue to match the cabinets....in any case i would avoid adding another wood pattern in this situation...

Thank you both. That's what i was wondering.

There are a few slate-looking options in LVP available. I did not find one I liked but that was nearly a year ago (and selections vary by geography). Alternatively, is cork an option for your budget and lifestyle? I wanted that to work for us SO MUCH but with dogs that tear thru the kitchen it wasn't meant to be. So far, our LVP has held up well ... it is hard to find non-wood looks but keep at it :)

refinish the 60 y old oak before anything. Mats are almost mandatory at a pivot point at a hallway like you show. what exactly is the problem with the kitchen vinyl floor? it looks fine and can take decorative runners and mats due to the neutral style. It looks as good as anything will if you are really going to have 3 materials. the thing to do after working with the old oak, is get a cohesive plan between the remaining areas, and kitchen cabinets and counters. You aren't showing enough to see how the different materials are playing off in the space.

@Pam A - we haven't looked at cork, I don't know much about it at this time. We do have a dog and there's lots of traffic through the kitchen at times, if that matters. I'll take a look at both slate-looking and cork.

@herbflavor - we hate the look of both the current vinly which has some stains and has started separating and the old stained oak but only have time & funds right now to deal with the kitchen. Else I agree with you. I'll add a couple more photos later today to show the entire kitchen.

How old is your house? I think those oak floors are charming and probably can be refinished...just $.02

The house was built around 1950. The old oak floors are badly water damaged in spots (outside the bathroom, at the front door, and a large spot in the dining room (from some plant, perhaps). Also, lots of scratches and squeeks.

Here's the whole kitchen. The dark wood entrance is to the back. The oak entrance is to the right and behind. Cabinets are dark blue. Walls are off-white.