Ask Mr. Smarty Plants

First, we need to get that neglected area cleaned up and made accessible for the plants you want. Could we interest you in making compost?  Here is an article from the Environmental Protection Agency on Composting at Home. When we first started composting, the Internet wasn't there, so we read paperback books, many of them still in print, such as the two listed in the Bibliography, at the bottom of this page.

Another idea for those leaves on the ground is to pile them up and run a lawnmower back and forth over them, with the cutting edge set down very low. You have almost instant compost; we suggest you read our How-To Article on Under Cover with Mulch. By taking those chopped leaves and spreading them over the weeds, you should be able to smother those weeds by cutting off light from them. You will need to sprinkle the leaves ever so often to keep the layers moist and not let it blow away.

Now, on to growing plants under those oak trees in the shade. Here is a previous Mr. Smarty Plants answer from San Antonio that could give you a good start. We believe that virtually all of the plants listed in that answer would also do fine in Tarrant County.

This member of the Smarty Plants Team gardened in Tarrant County for 38 years, and had a long-running love affair with compost. The house was newly built when we moved in, with poor soils compacted by construction equipment. Quercus stellata (Post oak) grew natively on that lot and it is likely that is what you have, too. Years of making mistakes (there was no Smarty Plants then), turning compost, putting down mulch and fixing mistakes resulted in a beautiful property - patience is key. There is no magic wand, but others will think you have one.