If you buy purchased mulch, it's much more affordable to buy it by the cubic yard from a landscaping company.  Many companies will deliver.  More economical options include shredded landscape trimmings (like from road maintenance crews), mulch hay, litter from stables, shredded leaves, grass clippings.  I agree, over time adding deep mulch will eventually improve any soil.  To OP, I might add that you might need to improve the drainage of your garden site, then build the soil from there.  Does water drain into the garden site?  Does the garden site get full sun?  Repeated tilling will slap that clay into an inpenetrable hard pan, so moisture can't drain below the depth of the tiller tines.  How big is your garden site?  How often do you till it?  Can you take part of the garden, or all of it out of production for a season to try to fix the problem.  You might try planting some heavy duty green manure crops to break up that hard pan.  Contact your local county extension service for a list of green manure crops that would work well with your soil.  You might also need to do some land work to route water away from the garden, and install some drain tile around the perimeter.  All expensive fixes, but in the long run worth it if the garden site is otherwise ideal.  It depends on how much you want to invest in the project and what your gardening goals are.  Lastly, is your garden in the BEST location for you to grow a garden?  I wish you the best of luck.  I had a garden that was a far cry from ideal, with too much shade and root penetration from near by trees, heavy clay soil, and it took way too long to dry out enough to work the soil in the spring.  I worked the soil for about 20 years, and it did improve, but not to my expectation.  I finally moved the garden, it now gets full sun, has a gentle south slope, the soil is sandy loam, I can get in to it at least a month before any of my neighbors can touch their gardens, and it produces much better than the old garden did, even though it is smaller.