Before you settle in on only people that are on the radio now, consider that there were MANY years on non pop-like country, and it shouldn't be ignored. I grew up on the country of the late 60's and 70's, and there were some AMAZING artists out there then.
Think Johnny Cash, George Jones, Merle Haggard, Willie Nelson, Tammy Wynette.
If you can branch out into a little rockabilly, look at Wanda Jackson. GREAT new album out now that she did with Jack White. It's awesome what he is doing with artists that the world has left behind and resurrecting their careers. Just look what he did with Loretta Lynn a few years back.
Of course you can never go wrong with Emmylou Harris, Dolly Parton, Alison Krauss. If you like a folkier vibe, check out Kathy Mattea, Mary Chapin Carpenter and Patty Griffin.