I'll take a crack at it.
St Augustine: most shade tolerant, average drought resistance, one of the fastest growing warm season grasses. Depending on what type you get, probably one of your cheaper options. Floratam is a very popular type and was developed partially by A&M. Sprig, sod, or plug.
Bermuda: not as shade tolerant, good drought resistance, quick growing, can take abuse like heavy traffic better than St Aug. tons of varieties from common Bermuda to tifway, tif 419, etc. Seed, sod, plug, etc. price will depend on what type you get.
Zoysia: less shade tolerant than St Aug but more than most Bermudas, good drought tolerance and requires less water than the other two, can take some abuse but is very slow to grow back if damaged, slowest growing of these three. Two main different types, a coarse and a fine leaf. Quite a few different cultivars: Pallisades (coarse), Emerald (fine), Zorro (fine), are just a few examples. Sod is highly recommended as if you plug it, you will still be able to see the plug spots possibly up to a year+ later. Usually more expensive than the other two.
Someone else can help you on the optimal establishment times, I don't have my 302 notes in front of me this evening. Each grass has its own advantages/disadvantages. My advice is no matter what you pick, if you want good & healthy looking grass, you have to put the time in and take care of it. No grass is going to look great if you don't water it during the Texas summer, fertilize it when it needs it, and be proactive in watching for problems or things that stress it.
Hope at least some of that helps.