A greige instead of a gray on the walls might be more neutral, but that depends on your style. White cabinets on top and blue on the bottom is fine if that's what goes with your decor. If you're talking about cool gray walls for the kitchen, they won't go with the warm walls of the adjoining room. Not sure where you want the gray walls - in the kitchen or adjoining room - you didn't specify. Gray walls are fine for a room that gets the warmest morning sun, but if not, a warmer color would work better.

I'd live with the kitchen for a bit before dropping the money to professionally paint your cabs and change the counters. You may want to go with a better layout. If you can post a measured 2D drawing of the space with dimensions you'll get more ideas.

The "sheen" can be easily remedied with a light sanding and a new coat or two of poly --flat or egg shell. That will hold up much better than any DIY paint job will. Cheap easy fix for now but I agree before any more effort/money is invested live with your space a year and see what rises to the surface as far a priorities.

He didn't say DIY. He said "professionally done" I'd stick to one color.............: ) and get a counter depth fridge too. With a single ( inconvenient) door swing. You know you can't fully open that fridge to get a drawer out, or to clean it, right? Or look into cutting back that wall.