Tennessee seems to be at the northern edge for short day and center for intermediate day onion "zones". So you may want to avoid the Walla Walla. You can't go wrong with intermediate. And you should be able to grow the Texas sweet, Georgia sweet. (In central Indiana I grow Candy onions which are intermediate. They are great, but I haven't figured out how to grow them BIG yet.)

If I were you, I'd suggest an intermediate. If you have room for two kinds, make the second a short day. You can always try different ones next year, that's what I am still doing.

I start my onions from seed, and some of the biggest I've grown have been Patterson. The Johnny's catalog does a good job of recommending latitude limits, then you can shop varieties from there. I get the best onions by growing long-days that aren't for the far north. In good years I can get Long Red Tropea really big -- not good storage onions, but my favorite for eating. I keep experimenting mostly because it takes me 3 years to use up a packet of seed and this year I bought a new supply. Trying White Wing and a couple of others from Fedco.

Well, the wife came home with some Texas sweet sets. I think they are short day. The fellow said to use a high phosphorus fertilizer, so I guess I'm going to grab some bone meal.

Any other thoughts?

Texas Sweets are typically White Granex. Short day type. Remember that an onion is basicly a leaf vegetable. They need an abundance of nitrogen to grow large. The onion bulb is a collection of the leaves modified base. The more and larger the leaves the bigger the onion.
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tn_gardening, congratulations on the onion choice. Lots of good advice here. You may want to look at the Dixondale Farm web site for their onion planting guide. It helps some with understanding the fertilizer.

you seem to be right on the line of day short vs day long onions. i recommend candy, it is day neutral, very sweet and stores very well.

Update:

2012 Fail
2013 Fail

I got lots of good, green growth, but my biggest onion was about the size of a ping pong ball.

I swear, I can't figure this onion stuff out.

East Tennessee you should be able to grow either long or intermediate day onions to size at least in the counties along the Virginia border. I southwest Virginia I had excellent results with Spanish types. Short day onions are for growing in the winter. Work fine here in Georgia. Had a cool wet summer this year and had a good crop of Spanish type (Golden Grande) but usually it gets to hot in June July for them to do much. short day onions are harvested in April and May and thus avoid the heat. White Granex is not a large onionbut grown in winter makes a decent onion.
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As Farmerdill pointed out earlier to you, onions are LEAFY vegetables, thus need a lot of nitrogen(+water).
I have planted Texas Sweet. They were about golf ball size for me too.

NOW of course, our discussion will not bear any fruits.