You will love cooking with gas and a Kohler sink is a good brand...

Regarding the backsplash question: I always prefer a very simple backsplash. They can look very busy if there is too much pattern. I suggest that you consider the simpler white subway tile that you show in one of your photos.

Another option is simple square white tiles set at an 45 degree angle.

I prefer a more basic/simpler backsplash versus the basket weave. A cast iron apron sink will be very heavy.....what color sink did you pick to go with your new countertop?

I personally always prefer a white sink..........It seems cleaner and always looks good in any kitchen.

i think of bathroom floor when i see a basketweave tile, so i'd say move along on that one, too.

you'll adore your gas stove!

not a fan of apron sinks, but i realize i'm pretty alone on that one.

I actually like the basket weave with plain counter the best with your kitchen. Your floor is blotchy so I would stay as plain as possible with the counters. The last backsplash is too modern for your kitchen

@kvedd, you really should go to at least one tile store, if only to see what is out there. Sometimes you can get a high end look with a less costly tile - like if you used subway with a herringbone pattern. Have you searched Houzz for an inspiration kitchen - that often helps week out the vacillating between choices.