Get to know your local tree cutters who work for the power company as well as the arborists who do jobs for individuals. Give them a place to dump their shredded trees and shrubs.
Be sure to have a place that they can dump, free of overhead powerlines and easy for a large truck to back into.
(Do get to know privet hedge, there are times of the years when privet gets cut back and the seeds, the millions and millions of seeds, are viable but easy to pull up until they are a year old. We did survive a couple of loads of wood with privet.)

You can always go to horse barns for "aged" manure and "used" straw.
Gypsum is about all you can use to break up the clay but the rock down there is another story.
Tilling the gypsum, manure and straw into the clay a foot deep would help tremendously.
Keep in mind that anything you put on the ground that hasn't decayed yet will suck all the nitrogen from your soil in an effort to decay.

We live up the road a bit from Lawrenceburg (Spring Hill) and have several places that sell loads of composted animal waste, although much it still needs some time to decompose. I bet there are several down there as well, but that's not free. There is an Amish community down there that you may be able to get animal compost from, of course they may use it themselves for their crops. Just think of all the great stone garden beds you can make with all the natural stone!

I've got some serious thick heavy dense red clay and just about nothing really helped for very long. The best advice is to get a sub-soiler and till in tons of compost several FEET deep.

Since this is not practical in a suburban garden, I have recently started using Oilseed Radish (Raphanus sativus or R. sativus var. Oleiferus) to punch into the clay. They have a thick, deep (12 to 24 inches!!!) taproot that can break up compacted soils; its lack of winter survival that negates the need for herbicide applications in the spring; and the belief that it contains allelochemicals -- chemicals released during decomposition that help control soil borne pests and weeds, and scavenge nitrate that has leached beyond the rooting zone of other crops.

Oilseed radish can become a weed if allowed to go to seed, either kill oilseed radish before it goes to seed or plant it late enough in the season to avoid letting it go to seed. If planted in mid to late August/Early September oilseed radish will generally not go to seed.

Here is a link that might be useful: Oilseed Radish - (Raphanus sativus)

Being a Lawrence county native (West Point) I'd have to say it varies on what you'll have. If this is in a new subdivision, then yeah, you'll probably have clay because they scraped away all the topsoil when developing it. (I simply can't understand the logic in that.)

If you are moving to an older house or property, you may be surprised with nice rich topsoil. And two houses next to each other may have totally different soil.

True there will probably some clay soil, but unless it is true Alabama red clay like sandquid has, manure, compost and gypsum are probably the best way to go. You WILL need a tiller if you don't have one.