What a fun project! When Mr. Smarty Plants recommends plants it is of the local native species; these can be reviewed by searching the “recommended species” list that can be found in the Plant Database page. You can also narrow the search by selecting the central region of the state of Texas, “Tree” as the general appearance, and then review the records returned for your fast growth and density [privacy] requirement.
As you might imagine, this gives a number of options; several that I like include Catalpa speciosa (Northern catalpa), which is fast growing but a bit tall, Cercis canadensis var. mexicana (Mexican redbud) for good color, Cotinus obovatus (American smoke tree), Juniperus virginiana (Eastern red cedar), Pistacia mexicana (Mexican pistachio), Quercus fusiformis (Escarpment live oak) and, for lots of color, Rhus lanceolata (Prairie flameleaf sumac). Another evergreen would be Texas sage, Leucophyllum frutescens (Cenizo), although it is more like a very large shrub, and also the yaupon, Ilex vomitoria (Yaupon), which will give you lovely red berries in the winter.
Here’s a few pictures of some of the more interesting of these.
Some of these may grow a bit big for a city fenceline. If you think so, you may want to steer the appearance towards “shrub” and look for some of the taller specimens. I’ve got a number of colorful favorites in that list also!