Find a well-rated local tile-and-stone shop and flooring shop. Take a drawer or cabinet door (like from over the fridge) with you so you can see what color ranges are appropriate. Take photos of adjoining flooring in other rooms. Plan on several trips including borrowing and returning samples.

Once you have scouted out what is possible, ask their estimators to come out to price new countertops, backsplash and flooring including professional installation. Flooring shops in my area do their own installation while tile shops may act as suppliers to professional installers.

1920s was huge for linoleum. If you’ve got vinyl now check out the options with Marmoleum. Tile would be fine but much more expensive and you have to worry about the thickness of the materials and transitions to other rooms.

Keeping your cabinets means keeping your layout, and that’s not great, so maybe think aome more about what you are willing to change and how much you are willing to spend.

We can't see what surrounds the kitchen, or even the entire kitchen.

That said? Soapstone counters would be lovely with the cabinets, a wood floor continued from the yonder we can't see might be nice, as could a porcelain tile mimic , of slate.

Before anything is switched? It appears you need a lot more lighting. The small island is cramped in, and I WOULD lower the breakfast bar to counter height. Before that? Make certain it is not cramped ( seems awfully close to the dining table.)

Make certain you love the way the kitchen functions, before you go to any tile or counter top/flooring fix.

"Colorful" can come from paint on the walls, from runner rugs on the floor, from accessories, and styling with color within glass door cabinets.

And yes......a backsplash . green is a natural : )

Have you considered taking down the floating cabinet to allow more light into the kitchen from the breakfast area?

Are you tired of the check floor? If not, you could be replace it with a dark cream, light cream combo would brighten the space and still look appropriate.

Jet mist/ Virginia mist granite will give you the vintage look of soapstone with fewer worries. Some versions of soapstone are bullet proof, some are fussy.

Do you know if the floor tiles are original? If so, be aware that they may contain asbestos.

It's so refreshing to see that you don't want to paint the cabinets, which are very beautiful!

I like the checked floor, and as eam44 said, you could replicate that look with Marmoleum. And Jan's photos of a green backsplash and dark counter tops are classic.

all of these will cost a fair amount of money, so doing more than that will push the budget.

I need to see the whole kitchen. Waht you are planning is costly so you better love the function of that space . the 1920s were not the same in what was needed in a kitchen compared to now. The cabinets you have are certainly not 1920s for sure . I agree the soapstone look counters or real would be nice . The tiles if cracking need to be replaced . THe flooring is another issue and do you know if it was original ? If not sure cover it do not attempt to remove it . The raised bar is IMO a bad idea in such a tiny space and thta hanging cabinet screams 1950-60s Removing that will make the space feel so much better . That island seems to be a big barrier in such a tiny space. You are in real need of good lighting too. If porcelain tile is the plan you have real issues to deal with since that choice will require a big job since that change requires the cabinets to be raised if you have a DW it cannot go back as it is ..

I asked chatgpt to give your photo a lighter floor and remove the upper. The floor looks great, it could not figure out how to remove the upper!

I have ceramic, not porcelain floor in the kitchen, and I hate it. And I don’t hate easily. It’s hard, things break when they fall on it, it hurts my feet, the grout is a pain to clean. It’s good points are, it’s cool in summer (but also winter, as it’s over an unconditioned crawl space), and water doesn’t bother it.

I plan to replace with vinyl or linoleum/Marmoleum.

I suggest a slate/stone looking floor tiles, warm white walls, white quartz countertops, new counter stools.

It you want to keep a checkered look, go for marmoleum in a diamond pattern. You can either keep the dark tones like you have now or go lighter as others have suggested. Otherwise, if your budget allows, I'd extend hardwood flooring in here.

If you are ok with darker and moody, go for soapstone counters or jet mist if you need to budget for granite. If you want light colored counters, I'm an endless fan of white corian, which can transition nicely in a more historic looking space.

I'd like to see your breakfast bar lowered to a single height countertop. I love your double sided glass upper.

what a great kitchen - I’d either run hardwood thru the kitchen or go with marmoluem -

fwiw we replaced linoleum with continuous hardwood in our ATL bungalow and the continuous flooring made the whole house seem so much bigger - they feathered in the new wood with the old and it looked like it had always been there

Soapstone counters would also be very nice just now sure about the lighting in the room...

Another idea for the floor is cork. You could get light and dark tiles and lay them in a checkerboard pattern.