WSU has published recommended lawn care guidelines for eastern WA that include seed recommendations, typically blends that include KBG as well as both creeping and tall fescues. Get your seed from local providers, not generic mixes found at the box stores. Most nurseries/garden centers will carry them as well as many feed stores.

btw, looking "nice and dark as possible" is a factor of watering and fertilizing, not so much the grass type :-) Cool season lawn blends, which the KBG and fescue blends are, naturally want to be dormant during the hot and dry summer months, so it takes effort and $$ to keep them lush and green all summer.

Establishing a Lawn in Eastern Washington

You should skip step 3. Tilling creates a fluffy soil of uneven depth. When it settles, it settles unevenly beginning on day 1 following the till and continuing for approximately the next 1,000 days. You are already ahead of that game if you do nothing and leave it alone. If the surface is uneven/bumpy, you can take this opportunity to scrape off the high spots with a hoe or rake and sweep that newly loosened soil into the low spots.

You might also consider going with a mix of prairie grasses like the western wheatgrass varieties, blue grama, and maybe some strawberry clover. If you let these go unmowed, it will become prairie, but if you mow once a month, it looks like a lawn. Here is a picture from a friend in Utah.