A powder room can have a bit more fun that the usual and honestly does not require huge amounts of storage so I would get a really cool piece of art above the toilet instead of shelves.I would stay away from grooved cabinets in a kitchen and really without seeing the old kitchen hard to comment on anything else.

I would go with a fixture with frosted glass. I'm not a fan of walking into a bathroom and looking at light bulbs. Did you keep the mirror that was there? if so it would be a good place to save a few dollars and rehang then frame it. Also because the electric was placed high to accommodate that mirror.

Is that whole now off-center, for the light fixture? The picture makes it look like its a tad off.

If so you will want to get something with a solid backplate, or at least as big as the one in the photo you shared so it can be shifted to the right a little.

If you did not keep the mirror that came with it ( which you could frame) I might be tempted to go with a satin nickel oval mirror so you can get some height and shape in the room.

I think also the light you picked is not so timeless kinda trendy, and might be a dust collector with all those little screws. IMO I think satin nickel would be a better choice.

This is a fixture that will be timeless and blends with about any style.

https://www.saxon-clark.com/quoizel-nicholas-vanity-light/nl8603bn-708/iteminformation.aspx