Call your local county extension office--they will have a publication recommending the best varieties for your area. I just googled a search for "best pecan trees for Tennessee" & it mentioned that they had one, (but not any specific varieties).
I'm in Louisiana, but we've had pecan trees in our family over 100 years now. I have trees in our backyard that my Grandfather planted that still bear, trees in the front yard that we planted when we built our house 30 years ago.
The newer varieties are more resistant to pecan scab and grow and produce faster. Fertilizing is important.
Pecans have "off" years, esp the older varieties--they will bear heavy one year & little or none the next year.
Our older trees are Stuarts, our younger ones include Cherokee, Choctaw, Sumner and Candy. We also have a few true native trees -- they produce a very small nut but very high in oil. They actually bring more $$ than the larger ones because of that.
We sell some of our pecans every year and put some up in the freezer--they will keep up to 2 years that way, shelled & put into ziploc bags.