Is that lattice on your ceiling? If that's staying, a fan would fit into this more rustic look. I don't care for fans, nor fans in kitchens, myself, but that's one of the options you listed. Your ceilings also don't look high enough for a fan, unless you can find a really flush fan. I'd have to see your chandelier. I lean towards a flush-ish, simple light fixture, since you have so much going on up there with the lattice. Like your appliances. Very sleek.

http://ths.gardenweb.com/discussions/2570333/cost-of-glazed-ceramic-tile-heath-pratt-and-larsonetc Looks like a hand glazed tile, maybe a crackle tile. You might find something similar by one of the manufacturers in this thread. You might also try contacting the tile store that nosoccermom identified.

I adore arabesque (and lantern. and other spanish -influenced traditional shapes-after all it's my favorite style ever, if I have to choose) but it doesn't spell modern to me.depends of course of what one means by modern because often people mean different things by that -some mean certain style, some mean something being more recent, contemporary. here's Fireclay tile blog..I liked glazed bricks on the first pic..second as well-shapes but less fluid shapes, more geometrical ones..and I strangely like this sweater pattern..I think last from the top? the one they call prep school. it might be too much and one needs to make sure they have enough space on their backsplash to pull it off. yet it exudes certain warmth..as if it was a sweater..:) https://www.fireclaytile.com/blog/ (as for the brand itself. I never used Fireclay myself, it's not inexpensive either, yet many people on these forums did, and remained extremely pleased with their quality. take a look at what they offer..they have many interesting products. including a lot of black plus white designs, some with a lot of contrast in the pattern, some, paler, more "barely there" of an effect)

You are going to get people's individual tastes and ideas, which might not be what you like. I went through hours of photos and narrowed it down to half a dozen looks that caught my eye. I then searched for the manufacturer of those tiles and which local tile stores carried them. I went to see them in person and ruled out a few of them right away, as the photos made them look warmer than they were in real life. As soon as my kitchen is at the same stage as yours, I will go and borrow the tile sample boards from 3 different tile stores. Look at them in my space and make a decision. Your question is very open ended, so you are just going to get a wide range of tastes and ideas. Maybe if you had some sample tiles in your kitchen people can be a bit more specific in their feedback.