First: Do you need to do a backsplash? I think what you have looks pretty darn good. I would consider leaving it. I don't know if I would want to pull that floor color up, personally.

Second: If you do want to do it. Do the running bond. Take a look at this thread from stacyneil where she did a simple white 4x4 in a running bond in a bathroom. It looks modern and fresh even though it's just a square repeated field tile. I don't know how much space you have and 2.5 rows (assuming you have 18" and don't remove the solid backsplash) might not look as nice.

I agree with brickton; my first impression looking at your photos was that your current backsplash looks nice and you don't really need to add anything more. What you have is/was standard in many homes (like my parents' and mine). BUT if you would like a tile backsplash just because you prefer that style, then I think running bond would look good. But I also agree with brickton that you might want to take a good hard look at the tile color on the wall before you commit; your paint color goes well with your countertop but the tile color might compete a bit (in my opinion).

I'll add another "leave it alone" to the pile. If you really want the function of a backsplash, though, consider another material or maybe just doing it in the area around the stove. A piece of sheet metal might look nice there, and it would be relatively easy to remove if a potential buyer doesn't want it.

Thanks everyone. Unfortunately, I need more of the functionality of the backsplash than necessarily just the style. We seem to always get all kinds of stains on the walls, especially behind the sink, and the paint on this house is flat and impossible to wash. The tile is the surround on my fireplace as well, and it looks ok, if not perfect against the color in there (which is the same as the kitchen). If I had it to do over again, I'd do a mosaic or even just a plain subway tile, but the tile is here and I have to use it.

Thanks for the validation on the running bond pattern, though. I feel better about it.

Ok, you guys kind of have me freaked out now, considering the tile I ordered is now here and, since it was special order, unreturnable. This is the same tile on the wall (fireplace) in the living room:

Is the color that bad? I'm petrified I'll not like this backsplash and my husband will be incredibly upset about that.

Sorry to be another "no" vote, but I wouldn't put that tile on as a backsplash, either. I don't think the tile is ugly, but I think it won't work well with your countertops and the short backsplash that's already there. I would consider putting up a stainless sheet if you only need it in some locations, or maybe glass/plexi.

Ok, we're talking about you finding a solution for 2 years. You already have the tile, you like it on the wall with your fireplace, and the same color paint is next to it there.
Your main goal is function and sellability. I think that tile will do the job for you, even if there are other ideas that might be good options. This is the one you've already paid for, and that's a big consideration in a two year forecast.
I would say use the tile and enjoy the ease of wiping down your backsplash. It sounds like in your house, a tile backsplash will be an upgrade in selling, and it obviously matches everything.
I agree that the amount of space you have between your counter and upper cabinets should determine if a running bond works in the situation or not. I prefer the running bond, but if there's not room for it, do the diagonal. It will visually raise the height between the two cabinets.

Don't worry! The tile will be functional and sellable. Like you said, when you live in a more permanent home, you can make a more permanent choice rather than one based on resale.