Start with the lighter walls. I have a similar style and tone cabinet and floor, but with oak cabinets. My style different - is an older vintage kitchen, but you can see how light the kitchen looks with lighter wall paint: https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~93784356 https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~93784291 When you refinish the floors, the yellowed finish will be gone and if you use water based finish, you may see a lighter floor. Your flooring guy should be able to make you up some samples - both of the refinished natural and some darker stains. Have him do more than one board of each since there is variation on how the different boards take stain. I did find these example of a darker floor: In my upstairs, the hardwood is a tad darker - gunstock rather than natural oak, but it still works with my natural oak doors. https://www.houzz.com/photos/my-kitchen-in-progress-phvw-vp~45783770

First things first: find out the species of your wood floor. We don't have very many room shots of the floors...which makes figuring out the COLOUR they will become once sanded/finished in a CLEAR COAT finish. What you are seeing right now is not a 'stain'. It is oil based polyurethane that has ambered (turned orange) just by aging. I would say there is NO stain on the floors. They are a birch (maybe maple....TOO HARD to tell from these slices in the photos) with a finish over top...no stain. The floor colour will drive the rest of the house. And yes...those floors in the kitchen are the very reason why we tell people NOT to put fake wood next to real wood. And the person who did it is probably colour blind. The clash of colours is enough for me to scratch my eyes out! But I digress. Personally I would find out the floor species FIRST. Then I would get a hardwood flooring professional to come in and offer a quote for the purchase of 'more' of the same wood (in the same cut, width and grade) and the cost to lace in the two floors and refinish them. That's going to be your 'big budget' ticket item. That will tell you what's left in the bank account. Painting out the trim is going to be a pain. The HEAVY graining of the red oak = doesn't look good when painted. I would assume you will need to remove/replace the wood trim unless otherwise convinced that something awesome could be done with them. I doubt it. Much of the trim looks like a patch-work-quilt that has been done a different times with different species of wood and different finish at different times with different skill levels. The doors on the other hand are a different story. If they are solid core, then they are worth a bundle. I would keep them and try to find a shade of stain or paint that would look handsome with the FINAL look of my floors. If you find out you have a VERY PALE wood underneath the orange oil based finish you might discover how pale they are when finished in a high-end two part water based finish (ahem...do NOT go with oil based finish or else you will simply end up with the same colour of floor = bright yellow/orange). I've seen Birch and Maple as well as red and white oak look as pale as wheat or dry sand. It is a markedly different tone compared to what you have now.

Hire a color consultant for advice. I don't think the current white is right--too much contrast--but there are warmer whites and other colors that will bring out the beauty of the wood. Here's a great, classic Houzz article on wall paints that work with wood. Your floors are beautiful and echo the wood trim. https://www.houzz.com/magazine/11-terrific-paint-color-matches-for-wood-details-stsetivw-vs~9025200

The counters look like they may be Corian, or a similar product. Although they do not do much for the wood of the cabinetry, perhaps, since they would be a significant cost to replace, use them as the basis for your design. I’ll suggest something rather daring, which is to add a deep periwinkle blue to the color scheme. Make sure to bring several paint samples home and hold them next to the countertop in different parts of the kitchen to see how it looks both in daylight and nighttime electric lighting. Paint any part of the wall you don’t tile including above the cabinetry. Honestly, if it was my personal kitchen, I’d paint the cabinets that color. You could paint them all, or a slightly lighter shade of the same color or white, just on the uppers is another option. Oak has a texture to the grain that “telegraphs” through the paint, and so you might want to experiment to see if you liked that, or the other option is to add the periwinkle blue to everything else, walls and backsplash. If you put up a tile backsplash, you MUST ABSOLUTELY remove the small existing backsplash first. Not to do so would be a mistake. If lie the idea o the color periwinkle, but are not sure about tiling or painting the cabinets, leave the corian backsplash, and paint the walls that color as a first step. I am certain you could find a pretty ceramic tile, perhaps a subway tile but with a deep bevel, to lend some interest, but look at other shapes and even combinations of tile. If you keep the cabinets the natural wood tone, do a periwinkle backsplash, but a white backsplash with periwinkle painted cabinets would be pretty, Here’s a white one from Lowes: