Welcome to NGA,
@KellyI !
You didn't say what type of mulch you are using (or thinking of using), but for a veggie garden I would recommend something that will break down and add organic matter to your soil (which I would think would be helpful for that red clay soil). My garden originally had very heavy clay-loam soil that always had standing water af, but over the years we've incorporated enough grass clippings, leaves, etc. that it is now loose and well draining. I mainly use grass clippings (from our rather large lawn) as mulch during the summer, and add a lot of leaves along with more clippings in the fall; over the course of the winter most of it has broken down, and what's left I can rake aside for planting and fertilizing. For some plants I add compost to the planting holes (especially tomatoes), for others I just side-dress with the compost and rake the mulch back over them.
I'm not sure whether the grass clippings would be a good mulch for you; some southern gardeners have mentioned that they don't use them because they cause grass to sprout up all over their garden. I think they were talking about Bermuda grass? Ours is mainly bluegrass and fescue. (This must be one of those things Stone was talking about that northerners have never heard of!) At any rate, a mulch will definitely help conserve the moisture in your soil, as well as suppressing weeds (and the weeds that do grow are usually much easier to remove).
Happy gardening!