M.F.
Wow. Not only could you be having culture shock moving from the Netherlands to here, but you seem to also be in "garden shock."
I would LOVE to have a garden full of the rich, colorful flowers I've seen in my travels abroad. But, alas, this is Texas and I have resigned myself to sticks and weeds. A native garden around here (meaning drought-tolerant and heat-resistant) will largely be different shades of green, with a smattering of color.
My husband has a master's degree in environmental science and has paid close attention to what grows around here and what never needs watering (and we've certainly tested this theory by never watering -- our grass is dead, but shrubs are fluorishing):
Texas sage (also called Silverado sage) is hugely popular here and will bloom all summer long into the fall (I am horribly allergic to it, so we avoid it).
Indian Hawthorne has rich green leaves with barely pink little bud-type flowers.
Crepe Myrtle provides lots of color early in the summer
Wax myrtle is another good one, but will only be green.
Mexican oregano is a nice shrub with purple flowers -- and you can cook with it! And it's evergreen.
Rosemary is nice too. It's only green, but adds texture to the garden.
Lantana is good for color and should come back every year. It's really hit or miss. We have some that survived the winter and some that didn't.
We also have a lovely little flowering plant similar to lantant called red skullcap. It has lasted 2 summers now.
Mexican Heather is also easy to care for and has purple flowers.
And we have a ground cover called "purple heart" that is good color. The whole plant is kind of eggplant colored.
It grows and grows all summer, then disappears in the winter and comes back in the spring.
My husband is also a big fan of yaupon (sp??) holly
We got a lot of great ideas from a nursery in New Braunfels called Schumaker's. Everything they have is native and/or drought tolerant/heat resistant. Granted, they get more rain further south, but we came home with a lot of new things to test in our yard.
Keep in mind that things which come back year after year in other parts of the state (or world) may only last a season here. My sister lives in south Texas and has things growing all the time that we have to re-buy and re-plant every year.
Also, one note of warning: A lot of people like to buy oleander for it's rich color, but they may not know that it's very poisonous. If you have pets or small children, you don't want this plant!!
Anyway, good luck! Happy gardening!