Some county landfills make compost and either sell it cheaply by the truckload, or give it away (but you have to load and transport it yourself). I'd check with your County Extension first, for the best source of a large amount of compost. Here they make fabulous compost and give it away for the taking. In Salt Lake City, where we made a garden out of a baked clay moonscape at my daughter's using 30 pickup loads of compost, it was $25 to fill the pickup - two scoops of their front-end loader.
The big thing about adding any natural amendment (anything that was ever a plant) is that it's made of cellulose fibers. Those fibers act like tiny sponges once incorporated into your soil, expanding when they get wet and contracting (to leave little air pockets) when they dry. What clay soil lacks is those air pockets. It's made of particles so fine they settle together and don't leave any gaps.
Compost is the best, because it's already partially broken down, so it's not stealing nutrients from the soil around it to decompose. Mulch decomposes faster if it's on the surface, and the fibers filter down into the soil eventually to add those fabulous fibers to the mix. You should always use lots of mulch, to keep your clay from baking into a giant brick whenever it's sunny.
Green manure, of the right type (usually a nitrogen fixing legume) tilled in adds lots of fiber but takes a little while to break down. I'd be tempted to do that in the summer and let it 'rest' while the heat and rain do the decomp job. From what I've been hearing of Texas summers lately, you don't want to do too much gardening in summer anyway.
