A question for my Texas friends

This is the kind of question that's best answered with careful research, but more fun to toss out on my blog. And considering that most of people I know who live or have lived in Texas are students of the life sciences in one way or another (including one conspicuously horticulturally minded individual), asking y'all isn't such a bad idear. (Whoops I mixed up my Texas and New England there.)

ANYWAY my question is: What types of fruit trees could one grow in one's small piece of Texas property, assuming that property is in that little Rhode Island sized segment region including Dallas/Ft. Worth, Austin, San Antonio, and surrounding space? And better: what fruit trees could one grow (or plant and have thrive) that make sense from an ecological point of view, that is, are not invasive and don't require input of too many alien elements such as water and fertilizer and such?

I asked this question of my Texas coworker, and she looked at me like I asked where I could store my flying saucer in Texas. (duh! Anywhere!) Eventually she remembered that there are trees that produce pecans and perhaps also plums, but couldn't answer my string of increasingly desperate and boring questions: "Avocados? Peaches? Oranges? Lemons?

It's one of the important side issues to the great "Where are we moving?" conundrum.