I don't think there is a variety that won't do well here.
The most common variety grown is the Concord, which I believe is an American native, the second most common is the Muscadine and Scuppernong which I know are Native.
Any Co-Op feed and seed store and the box stores ( Lowes, HD, Wally's etc.) usually have several varieties.
Most seed catalogs ( Guerney's, Parks. Henry Field's, Shumways,etc ) have them at better prices. It's a little late in the season to be ordering now but they will still survive if planted soon.

Thanks. I think I grew concords in Huntsville in the early 80s - they were already there when I rented the place. They made great grape jelly! Some of the grpes would split while on the vine, and the juice would ferment; the bees would drink the juice and get drunk!

I assume they need to be planted in early Spring, so I will wait for next year.

A gentleman I knew and worked with, who passed away several years ago, had a "hobby farm" up at Guntersville. In the summer he would call me at work and tell me to meet him at the loading dock. He would have 5 gallon buckets or Concord grapes and muscadines in the very spacious trunk of his huge Cadillac sedan. Almost every year his Concord grape vines were full of grapes. He swore by the Concord variety. All Ie had to do was to bring him a few jars of jelly or jam and he was happy until the next crop.