If you've got plants that you started inside, whether cilantro or something else, you generally have to get them used to being outside gradually: before transplanting them out, put them out the first day just an hour or so, the next day a couple of hours, the day after maybe a half day, then you can plant them out. Full sun is a lot stronger than even proper plant lights and they need to get used to it.
Cilantro is going to bolt whatever you do; some varieties faster than others. Get seed of a strain meant for leaf, not for seed production; but it'll still bolt. I never grow that from transplant as the shock of transplanting can bring on bolting even faster; I direct seed it. And yes, you need to do succession plantings; about every three weeks is good.
There are a lot of different kinds of basil, with different flavors. Some might do better in your area than others (I've got no useful advice about Texas in particular, I'm in upstate New York.) Basil generally likes it warm, though I don't know whether some strains don't like it too warm, we don't get out of the 90's F or at least I certainly hope not, I don't like it that hot myself. It's very frost tender. Bolting's not a problem with basil; just keep cutting it back as you want to use it. Unlike cilantro, the flavor won't change if you don't cut it back enough and it goes into bloom. Basil flowers are also edible, and can make quite a pretty garnish.