Probably something like a mix of kentucky bluegrass and fescue will work well for you (I'm in eastern MO myself - outside St. Louis).
Actually, if you just go browse the grass seed aisle at Home Depot, you'll see that there are different varieties that are better suited to shade versus full sun, and so forth - and you'll probably get a better feel for what you should do.
Proper fertilizer at the right time of the year, and weed/disease prevention will go a long way towards a nice looking lawn (as well as correct watering, of course). You can plant the best seeds in the world, and the lawn will still look like crap if you don't take proper care of it. I say that because the houses in my neighborhood probably use very similar grass (if not idenitical), but there's a HUGE difference among laws depending on who takes better care.
For example, my neighbor two houses over already has a nice green lawn, because he remembered to put down pre-emergent fertilizer a while ago. I was late getting it down, so mine is still pathcy and yellowy in spots.
I am BY NO MEANS an expert on this, just passing on my limited understanding.