Rosemary should grow well for you in Texas - it may even stay all year long for you. Both rosemary and basil like lots of sun and staying dry. I was wildly successful with parsley last summer (in fact I had way too much) but I think it requires staying a bit cooler.
I think herbs are so much fun to grow because, they can withstand a lot more neglect than other vegetables and flowers. And that's great for me, because I always go into spring planting with grand aspirations, and by mid-July when it's hot and humid out, my interest seems to be more in staying next to the a/c with a cool drink and a magazine.
Many herbs are perennials, so you need to plan in your head how much they can be expected to grow and leave enough room. Other herbs that are really low maintenance are oregano, thyme and sage all of which will keep coming back. I like to mix in the oregano and thyme around the other plants because it is low-ground cover and looks pretty and helps keep weeds out. However, you have to wash it really good before using it!
To get nice big, fat basil leaves you have to be pretty regular about nipping out the little flower buds that will grow, or the plant will get too scraggly. This happens about the time that I have lost all desire to swat bugs and play in my garden, so I've never been to successful with basil and tend to just buy big bunches of it at the local farmers market. That way I can feel good about supporting the local economy and stay cool!
Tracy
ETA: Jes, do give herbs a try...they are quite easy and much cheaper than buying at the store. There is a great on-line site for seeds called
www.nicholsgardennursery.com that has tons of different types of herbs.