I like the grain in the first flooring sample and the grey in the first tile.

I'm saying the same, number one and the gray.

I like either of the first 2 floor samples and I'd want a plainer tile for the BS. Something with no pattern/movement on it. I think it'll fight with the granite. A very light grey or even cream tile.

My vote is for the second choice for the wood floor. The subway tile is difficult as our monitors are not always the same. Go with the one that blends best with your counter.
The BS should relate to something in the room and in your case it would be the counter.
Because the BS choice is critical, can you do a sample board? This has helped so many here make a better choice. You can then leave it up throughout the day. One tile sometimes is not enough as color can play off itself. Fir example, one tile can look great alone, but with others you might get a pink undertone.

I like the third floor sample, and the first tile sample.

It's funny the way the camera views things differently. IRL, the 3rd wood looks much closer to the tile color, but I'm not sure that's a good thing. The dark floor we have now really shows the dust - not good for a lazy housekeeper such as myself. I do fine with the halls and kitchen, but I don't even notice it in the big room, probably because I seldom go in there except to walk through it.

Another thing I've been wondering about is the feel of the wood. Our current floor has, or had, a smooth finish. It didn't look plastic, but had an obvious finish coat on it. The first two samples here don't have a smooth finish at all, almost like they need to be sanded a little more. The salesman said they have a scratch resistant coating and they are hand scraped. The third sample has a finish that feels smooth, more like furniture.

I like the grain in floor #1 and #3, but I like the colors of #2 and #3 next to your tile. Since #3 is darker and you were hoping to go a little lighter, I would probably go with #2. I think the color of #2 actually looks the best next to your tile.

I know what you mean msrose, I like the grain in #1 best too. But we are going with #2 I think. I think it will blend best with the tile and we like that it doesn't have a high gloss.

Now the hard part is convincing dh to widen a doorway and paint. Perfect time to make changes I think.

I like the third wood floor sample the best with the tile it's pictured with. The darker tones in the tile are repeated in the wood tones. It's dark, but I don't think you achieve anything by picking a lighter toned wood if it doesn't harmonize with the tile. Could you look for a lighter toned wood that still has a dark grain outline?

Maybe it's just my monitor, but neither of the backsplash tile colors are picked up in the granite countertop, which I assume is already picked or in place. It's difficult to choose between similar colors from a monitor picture!

It is hard when it's a photograph which doesn't necessarily read true, and then on a monitor which also changes the colors. In person, the overall color in the 2nd blends with the lighter color in the tile. Also, it's a matte finish which also looks better with the tile than the gloss. That was one thing that bugged me about the current wood floor. And the 2nd is also just a bit lighter than the 3rd and the original, and we hope that will make the big room adjoining the kitchen a bit lighter. It always seems dark now.