When people say "traditional country" music they're usually referring to styles that were most popular in the '50's and '60's, even though no one is more traditional than the (Original) Carter Family who, along with Jimmie Rodgers, were country's first superstars. (Various offshoots continued as The Carter Family for years - hence the importance of distinguishing the original trio of A,P., Sara, and Maybelle.) Even today, as surely as two males harmonizing are compared to The Louvin Brothers, male/female harmonies are compared to The Carter Family - often by people quite unfamiliar with the genuine article.
One problem in getting familiar with The Carter Family is the sheer volume of their oeuvre. This 20-track "American Milestones" issue of recordings made in 1935 (and a few from 1940) may be a good place to start. It includes many of their most famous tunes - "Wildwood Flower," "Keep On The Sunny Side," "Worried Man Blues" and the title track. As old as these recordings are they're actually pretty well along in the group's life. The original versions were made for RCA in the late '20's and early '30's. By the mid-'30's, Sara sang in a lower voice and recording quality had improved, so these later recordings are preferable for many people.