Can you post some more pictures of the bathroom as it's hard to really see what's going on with close-ups?

If you're thinking of a brown, here are a few very nice colors. I use Behr paint because of cost, but I use Sherwin Williams for examples because you can link from their site to this site. Any paint company can mix any color for you if you get the color code.





Go to Sherwin Williams site and upload pictures of your bathroom to their color visualizer program where you can apply color. It isn't perfect, but it does give you an idea of how a color looks on a wall. I've noticed that the colors are lighter on my walls than on the swatch so don't be afraid to try darker colors than you think would work.

https://www.sherwin-williams.com/visualizer/#

I love the floor tiles. I would use that as your inspiration. I'd paint the wall below the chair rail and the vanity a dark warm gray to pull in the tile and a color about 3 or 4 shades lighter above. I would consider better lighting also. Currently it's very yellow which is not flattering. Something in the white light range would be better especially for such a small space. The chandelier is also distracting and hangs too low. To update the mirror and towel rack consider enamel paint. I'd go bright white semi-gloss.
In the future I would consider a solid surface counter, new sink, faucet and new vanity. Instead of a backsplash I would carry the chair rail trim all the way around.

Cheers.

A dark color is going to make it seem even smaller. What do you think about white on the bottom and a graphic paper with brown/white on the top section (or paint brown to compliment the floor). You could spray paint the mirror and chandelier white and change the handles on the cupboard for a more updated look as well. In the past, we have several times painted our countertops with a melanie paint and it wears really well (would suggest white) and will tide you over until you're ready to redo the bathroom.
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Here's as big as I can get

Yes, Leslee - they are brown floor tiles. I actually like them a lot - the colors of the pic you attached are sort of what I had in mind...thanks!