there are so many great backsplash tiles to choose from.

It depends on your style. colors you love, etc. the green and white is great, a neutral that will look great with any color. Just depends on what you like.

The black pulls look good, even a brass would be pretty.

I always like to choose something with a bit of shimmer to brighten up the kitchen.

... as far as that blank end space, you could add a cute shelf unit or even just a framed picture to fill the space.

^great start above

I would move the microwave and add an oven vent in place of that shelf. I would consider that to look more finished than the microwave in that area.

Don't paint the cabinets. Yours look good. Because you have black exposed hinges, and they look good, stick with the black hardware you already have. They add a nice bold look to the cabinets.

Paint the wood shelf the same as your cabinets. Do you have a large object to put up there?

What direction are you leaning for tiles? Do you love / hate anything in particular?

The small floating shelf looks crammed up against the cabinets, and the black brackets draw your eye and not in a pleasant way. I would remove that shelf and install two floating shelves using hidden brackets. I would make the shelves long enough to fit against the cabinet and extend to the end of the countertop. There are many kinds of hidden brackets; look at Sheppard Brackets and choose a size that's appropriate for the boards you plan to use and the amount of weight you want to put on the shelves. If you can't do it yourself, enlist a handy friend to help or a local competent handyman.

With respect to the microwave -- as much as I dislike over-the-range microwave ovens, it looks like that is the only place where you can place one, other than on the countertop which would take up counter space. Ideally -- a microwave with a vent and light would also solve the problem of needing a vent for the cooktop, assuming it can be vented to the outside through a wall or through the roof. A slide-in range and oven with an over-the-range microwave would have a more streamlined look than what you have now. It would require removing the shelf above the range and anchoring the microwave to the cabinet above. A slide-in induction-cooktop oven unit with controls along the front of the unit would allow for an uninterrupted backsplash behind the range. Again, a skilled handyman could do this -- the only issue would be venting it to the outside.

i think I'd pick a patterned tile..there are many...subtle or colorful/ some bold ones too. the cabinet color is very easy/ not a statement .... so blend something in there w some visual.

here are a couple..just bring home samples

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I'd add some under cabinet lighting and choose a glass tile backsplash in a complementary color to brighten the space.