As other posters have said, this will depend largely on your application. But the US South is extremely diverse. There are hundreds of accents. A dozen or more dialects at least. And many, many cultures.
Let me give you an analogy to put it into perspective.
Let's say you said that you wanted to know which Native Americans were the most Native American. And you wanted to know which groups had Native American languages/accents, customs, and traditions.
Except for broad anthropological classifications of which populations were in the US before European settlements, lumping them together as a collective is silly. It erases the important distinguishing characteristics that makes each group a rich and important part of our history.
The Dineh (Navajo) in what is now Arizona, New Mexico, and extreme southern Utah will have a very different language and traditions from the Cherokee (some of whom remain in western North Carolina, many of whom were forced to relocate to Oklahoma by walking the Trail Of Tears). Yet both populations are Native American.
The US South varies greatly from region to region. Factors that contribute to this include, but are not limited to:
1. The origins and customs of the "original" settlers.
Some places such as Charleston, SC are a wealth of diverse cultures, including descendents of French Hugenots, and the Gullah from West Africa, many of whom make their livelihood to this day by selling their handmade baskets in the town market using the same techniques their African ancesters have passed down for generations. By contrast, central North Carolina was populated largely by Scots-Irish and Germanic settlers, though there are notable exceptions such as the Moravian settlement in historic Winston-Salem which still exists today.
2. Economic and war history.
The outcome of the War Between The States played a major role in any given area's current economic and political climate. Since some towns like Raleigh and Charlotte were spared most of the brunt of Sherman's army (and the subsequent fires set by the locals to destory supplies so they would not reach Union forces), it positioned them for quicker recovery and the ability to grow -- whereas other areas of the South never have fully recovered.
If, by "most Southern" you mean the closest in traditions and mindsets to the Antebellum era (pre-Civil War), you will probably find pockets of areas in Mississippi, Louisiana, and Alabama that come closest to the bill. But again, there is a lot of diversity there. New Orleans is a blend of cultures like Charleston is, yet it's quite different. Jackson, MS is a thoroughly modern city. The collegiage town of Oxford, MS hosts one of the South's most distinguished universities.
You can make a caricature of someone in a 10-gallon hat sipping juleps on the front porch, but if you want a 3-dimensional character or setting, pick an area of the South and research it. The more you know, the more believable your choices will be. Outside of the United States, people often make reference to someone having "an American accent", and I think few Americans will argue that that is a rather sweeping classification to make.
A person from Brooklyn, NY will sound drastically different from a native of Madison, Wisconsin, or Boston's Back Bay area.
Same with Southerners.
Incidentally, don't visit Southerners and ask who are the most or best Southerners. It's like asking New Yorkers and Chicagoans who makes the best pizza, or Texans and North Carolinians who makes the best BBQ. You'll start a war.