You can study the breeds from the links Rhoderunner gave you. They can be addictive and, if you are like me, you'll change your mind often.
You sound as if you are more interested in chickens as pets and conversation pieces rather than for meat or eggs. I'd still suggest full sized fowl for you.
The larger the chicken the harder it is for it to fly. A bantam could clear yout fence no problem. A grown full sized fowl could if it were really motivated, but you'll have a lot better luck keeping the larger birds in your fenced area. The young ones can fly pretty well but they fly less well as they get heavier.
You mentioned easily tamed. It depends on the personality of the individual birds, but you're more likely to be successful with the larger birds.
You mentioned quiet. That means you don't want a rooster. As far as I know, My Pet Chicken is the only source for sexed bantams if you get chicks. And I think you want chicks since they are easier to tame.
In your situation, I would think you are not going to hatch chicks, so you do not want a breed that goes broody a lot. Again, this points to larger fowl, although there are some breeds to avoid. The Orpington and Cochin come to mind. That's unfortunate because I think either would suit you well except for broodiness.
I agree with Rhoderunner. Chickens are social animals. You really should get at least three. You should check your local regulations if you haven't already. You may have restrictions on how many you can have, distance from property lines the coop has to be built, or maybe even if you can have chickens.
All hatcheries have a minimum number they will ship, usually 15 or 25. That's so they stay warm enough during shipping. You'd have to check each hatchery for their requirements. Once you select the breed or breeds you want, you could advertise on this site to see if anyone wants to share an order with you or you could look for someone in the Houston area that might sell you some chicks if you will come to pick them up. If you buy them from someone local, you might want to get some old enough that you can tell the sex.
I'd suggest you go through the Henderson Chart and pick out breeds to consider, then cross-reference them on Feathersite. As long as you provide shade, good ventilation in the coop, and plenty of water, practically all breeds will do OK in the heat.
You may want more than one breed or at least different colors of the same breed. We all have our own definition of ornamental. One breed I'd suggest you consider is the naked neck. It's not for everyone. Some people consider them very ugly, but some like them. They are certainly a conversation piece. Brahma also come to mind as a possible good fit but watch the coloring. Some are flashier than others. The Speckled Sussex is another to consider. But there are several that will suit you.
I would not totally rule out the sex links either. These are crossbreeds where the sex can be determined easily at hatch, usually by color. They will not show up on the Henderson Chart since they are crossbreeds. They lay a lot of eggs and may not be as flashy as you want, but I think they are worth considering for your circumstances.
Good luck, whatever you decide.