Congrats on your "new to you" home! Always best to post as many pics of the space from different angles as you can.
Re: backsplash, unless you're planning to replace the countertops, you already have a backsplash & no need to add anything above it :-)
Re: wall colour - is the kitchen open or closed to adjoining spaces? That will factor into paint decisions if open. If you're looking to brighten up the space, certainly a lighter wall colour will help (a warm white would make the cabinets pop) but also consider your lighting - overhead & undercab (if you have). Replacing all bulbs with 4000K LED will make a big difference.
Finally, lots of pics on Houzz to inspire you so have fun & post your after pics.

Congratulations on your new home!

Can you post additional photos from other angles?

there are possibly no glides on the drawer frames. there may be only one fixed shelf on the lower cabinets. I might just live with this for a while and look at the whole space you have available for some sort of renovation in the future. If the entire footprint of the kitchen space will remain small as you mention "small" ..then efficiency is really important long term. Dont sink too much money into this right now.

I agree on holding off with anything major like a tiled backsplash until you’ve lived with it for a bit and know first whether you’ll be making any major layout changes due to upgraded appliances or the like.

If you love MCM, I might eschew the currently fashionable grayed paint tones and go for full-on color like bright teal or jade green, which look really stellar with the knotty pine:

As Andrea noted, that 4 inches of counter material going up the wall IS a backsplash, and generally you wouldn't tile above that (it's either/or, not both). If you installed a new countertop, you would be able to install a course of tiles under the window (and if you removed the wood valance and if possible the soffit above the window, you could tile above the window as well), BUT at that point your getting into $$$ and you have to ask yourself whether it's better to just wait until you can do a full remodel (it depends on how well the layout works for you and whether there are other issues with the kitchen).

I don't see anything wrong with the 4 inch backsplash you have and paint above.

I love the cute cottage look to your kitchen. I would use a lighter aqua, turquoise, teal paint on the walls. Circus Peanut has posted pictures above. One does have turquoise walls, although, I think that color is a bit too dark for your space. I would pick a color about 2 shades lighter. Congratulations on your new home.

this is a charming kitchen. I assume you are keeping everything for now? thank goodness that formica countertop is a relatively neutral pattern and color! between this and the white appliances, I don't think the warm green is working. I really like Circus Peanut's advice to look for a fun teal or a lighter shade of cool green (such as sage).

the cabinets are beautiful and I really hesitate to suggest painting them but...

the black hardware looks really harsh here. swapping it out is going to be problematic -- wood darkens over time, and hardware shields it, leaving bright spots. you have to find the right size of new hardware that covers that up. you could have them sanded down, but that's a lot of work and you would still be stuck with strap hinges since the holes are drilled all the way through. if you could find the right hardware, I think a dark satin nickel would help tone down the cabinets.

however, finding just-right new hardware might be fairly tricky. and those cabinets are really.... piney. if you painted them, you could fill the holes and put in whatever hardware you wanted, including way smaller semi-concealed hinges. and a lighter color would work so much better with the light counter/appliances/floor. it would solve a lot of design problems here. in that case, I'd paint the cabinets teal or sage, and paint the walls white. (also, I'd remove the curly valance, or cut it straight, but that's just a personal preference.)

you have two major issues: A: outdated looking countertop/appliances (which might be perfectly functional). B: super country bumpkin 50s cabinets. they just do not play well together. to make this kitchen look better, either A or B needs to majorly change. if you can't (or won't) do plan A, then painting the cabinets is going to make the biggest visual impact on a small budget. it could look really cute!

Wow, thank you ALL so much for all of these helpful replies!! I have to admit I had no idea the 4 inch of counter was considered a "backsplash" so that's great to know! Eventually we will want to update the countertops but I'm not sure if that's in the budget right now. I agree with those who said we should live with it for a bit before making any major changes - of course I am always just itching to make changes and customize everything!

@User I REALLY liked your suggestions about changing the wall color to a cooler tone, and I actually like the idea of teal. But, your comments about painting the cabinets *really* have me considering it. Especially considering we don't have plans right this second to change all appliances.

I really commend you for keeping the appliances. if they still work well, there's no shame in that! if you think you'll only have them for a few years, you could paint or wallpaper them. google it! (it's kind of experimental, but could be fun as a temporary solution.)

here's some inspiration for painted 50s cabinets paired with light color counters / appliances:

this one might be too white since your floor is also white? (you could do color for the lowers and white uppers.) see how the valance above the sink is squared off.

this green is a little to bright for my taste, but still, this kitchen is adorable.

I had similar hardware on my cabinets when I bought my house) I was able find a simpler design, more to my liking, that fit the holes and covered up any discoloration/marks - but selection wasn't vast, I will admit. Unless you love that look of course!

I think that removing the scalloped wooden valance above the window (just the lower part) will help the space feel a bit more open/larger.

I agree on no tile until/unless you change out the formica counter. But then, if you do, the right selection of counter+tile can really make the cabinets look good (as the right paint can, as mentioned above). I think that the green paint currently there is indeed too dark, almost drab, for the space. I would go for a pale green-blue, or a warm white (Simply White is one fresh white that works very well with knotty pine). No tans or distinct yellows, contrary to what is often seen.

The cabinets can be retrofit with better shelving if needed, and even with pullout shelves or interior drawer -but at the sacrifice of the space behind the face framing.

Oh, I love your kitchen! It's definitely an original 1950s knotty pine kitchen. Check out the website retrorenovation.com for tons of inspiration and history about this type of kitchen (a page featuring different vintage kitchens is here, lots of great inspiration!).

I agree that a pretty aqua color would go well in this space. And if you ever do end up replacing the counters, laminate is period correct and relatively cheap. If you do that, select a counter without a 3" backsplash and then you can do a 4" square tile backsplash for a period appropriate effect. Stay away from quartz, granite, or other stone countertops as they would all look out of place here.

Since some people have come out in favor of painting the cabinets, I want to mention the technical challenges of painting knotty pine. Knots tend to bleed through paint, so if you go that route, be sure that you know what your getting into and research how to seal the knots before painting. Sorry, I don't know the solution, I'm only aware of the problem.

We might recommend living in the space for a bit before doing a lot of updating, however we might recommend updating the hardware, flooring, and adding a roman shade to the window if you don't want to replace the appliances.

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yes, agreed with cawaps. at least they're slab front and there's not many of them. not too huge of a project. totally worth the elbow grease.

Those cabinets look to be in great shape and have so much character, I wouldn't paint them unless it was really necessary.

I’m so appreciative of everyone’s thoughts and suggestions on this thread, truly!!

I wouldnt paint the cabinets either. Do some research, on 50's kitchen. Keep it retro. Since I had kitchens in the 50's, I am very familiar with kitchens that looked just like yours. A lot of them, were aqua, or teal too. It was a much used color in kitchens in the 50's. You have a chance to have a unique kitchen, that doesnt look just like everyone elses, take advantage of that.

I would change the floor to a minty green linoleum. Add some retro minty appliances, Think smeg but purchace knock offs, and remove maybe a top door to create an open shelf feel and display festive wear dishes. Two exampkes of young families embracing their retro kitchens.

before

after

Oh my friend painted her white fridge turqouis and it looks really cool. Alot cheaper than smeg or big chill!

The cabinets are very dominant and to make the space come to life, a think a dark wall will work much better with all the orange tone wood...I'm thinking black. There isn't a lot of wall exposed, so you are not creating a dungeon; you are achoring the cabs...something like this photo to show the contrast:

You have so little counter space, changing it out to black would be stunning and reasonable.

Check out this new Wilsonart laminate. Huge difference from the peeling, seamed stuff of years gone by:

The last photo that roarah posted looks like the wall paint is close to the shade I have in my kitchen (no knotty pine there). It is Valspar "Ante Meridian" and is a shade that plays well with a range of colors from dark blues - pale blues, to aquas and turquoises.