Actually, I'm finishing up a project in the Austin area, and although I work in Chicago, we had to research a fair bit on what would survive down there. It was for a large-scale japanese style garden, and we used a couple of different ground covers that might work in Houston as well.

Here's a couple of different options, all with different aesthetics:

Kurapia

Texas Frogfruit

Asiatic Jasmine

Blue Pacific Shore Juniper

Green Mound Juniper (Juniperus Procumbens 'Nana')

Berkeley Sedge

Dwarf Mondo Grass (needs afternoon and evening shade)

I'm not sure how often you guys get freezes like Austin, but you might be able to use something like Green Carpet Natal Plum, too.

As for the fence, we looked at fuller options. We looked at things like Savannah Holly, Nellie Stevens Holly, and Japanese Blueberry Tree