I think you could definitely find grays and a white that would work well with that counter top. And if you are getting rid of the flourescent light, then it doesn't matter that the tile you like doesn't work with flourescent. Maybe changing your light to what you do want is the first step. Do you have undercabinet lights?

I think more pictures, from a bit of distance, would help. I like the backsplash you chose, but it will be much busier installed than you realize, and some people consider the style to be dated. If you are going to paint the cabinets, I think you should do that before making any other purchases.
Wood is problematic as a flooring material, it gets dinged, scratched, and damaged by water. But none of that bothers me as much as tile floors. Tile, even on top of a slab foundation, is much harder to stand on and on things which drop. It is very messy and expensive to have ripped out once installed. Wood floors age and still look beautiful, tile just looks dated.

I think both those choices would look great on white cabinets! I am all for bucking trends and if you like it you like it, use it!

I do agree about the lighting, though it is pretty easy to get flourescents (I think?) in a natural daylight spectrum. I am pretty sure about this because I shopped for flourescents for seed-starting and they come in a much wider variety on the spectrum than I would have guessed.

I think the tile looks great with the countertop. Mixed mosaic tile back splashes don't get a lot of love on this forum. Most often they are declared as too busy or too trendy. I say go with what you like. As you know, since are changing your current backsplash, the mosaic tile backsplash could be changed out too if you get tired of it or if the next buyer of the house doesn't like it.
I didn't worry at all about installing a mosaic very similar to yours in my kitchen. I actually bought my tile before my kitchen was even demo'd. Here is a shot of my mosaic:

Definitly check out other lighting options and look at the color temperature. The higher the number the whiter the color. The highest numbers though can look almost blue. Check the lumens as well as the color rendering index CRI.
Color rendering index (CRI) is a measure of how accurately an artificial light source displays colors. CRI is determined by comparing the appearance of a colored object under an artificial light source to its appearance under incandescent light. The higher the CRI, the better the artificial light source is at rendering colors accurately. High (above 80) CRI is preferred in the home. ENERGY STAR requires that qualified fixtures have lamps with CRI above 80. Cree's newest LED bulbs have as CRI of 90.

Thanks everyone for the inputs!

I do like the backsplash and I am not too worried about it being too busy as it has clear and silver tiles and only one dark color on there which is the dark grey tiles.

My kitchen is on the small side, it is a galley kitchen and I am a bit worried about making it too busy..but I thought with the light reflecting off the stainless steel or silver tiles of the backsplash and the clear ones plus coloring the cabinets white and changing the floor to matching tiles will make it look nicer? Also I have plans to change the sink to a stainless steel one.

I have two other pictures that I can add and I will take better ones during the day.

Yeah, I do not see it being that big an issue since you are isung white cabinets. It is not my personal style, but I think it adds the right amount of bling! It is such a trick to avoid "boring" in a white kitchen. You would pull it off beautifully!

"under the kitchen light (a fluorescent light) which I plan on changing the colors seem like they won't work."

Take the time to bring in a light (LED or whatever you plan to use) from somewhere else, or buy a "Daylight" flourescent tube and change tubes.

this is a BIG choice and you don't want to make it under conditions you know are bad.

I see you've got ye olde tiled side splash. Don't tile that on your redo. It's not a current look. Also remove the short granite splash if you can.

Congrats on your new house! I think your backsplash will work since you're painting the cabinets white. I agree with lazy gardens about bringing in different lighting before you make a final decision. It will really help with color decisions, if not for the backsplash itself, it will for what color white you paint the cabinets.

Also, wood floor in a kitchen is fine. Many people have it with no problems. Tile is good too, but is harder under foot, so if you do go the tile route, I'd look into getting a gel mat to stand on for in front of your sink and/or where you usually stand to prep food.