Lived in Houston for over 20 years, married to a Houston native. He drives a Scion Xa (small hatchback) and loves it. Good friend of ours drives a Honda Fit and loves it. I drive a Nissan Rogue (small SUV) and love it.
Don't get a certain type of vehicle just because everyone else says you have to. Find one that fits your needs, has good safety features, is priced right and gets great gas mileage and don't forget to factor in the insurance costs as well.
As long as you drive defensively and are aware of your surroundings, the standard safety features of most smaller cars will be enough to protect you from most crashes. You can get creamed just as easily driving a truck as you could driving a sedan if you have bad luck.
Not going to sugar-coat this: Houston is pretty awful as far as poor drivers - we apparently won worst drivers and rudest drivers in the last couple of years (sigh). You need to be scanning and aware of intersections (lots of red light runners), asshole drivers that cut across several lanes to reach an exit or stop suddenly (don't tailgate - 2 car length minimum if you can!), and if you miss a turn, just go down and turn around when you can... cutting someone off can spark road rage, and Houston assholes love their guns too. (double sigh).