This should be your first and most important question. You want to make sure they are properly insured and that you will not be liable for any damage, accidents or injuries.
Any professional tree service company in Houston will be happy to share a list of satisfied customers. Ask for customers that they have done work for in the past month or so; you don't want ancient history.
Get written estimates from at least three equal companies to compare prices and understand the scope of the job, which leads to the next question.
You DO NOT want massive power equipment driving over your lawn and flowerbeds causing collateral damage. If they are going across your lawn, make sure they know the locations of sprinkler heads or other objects that may be damaged.
It may be a good idea to take pictures before they begin so you have a record just in case there is damage. Make sure you understand how they will clean up during and after the job.
This is why getting an estimate is VERY important. One company might say three days while another company says three hours. I would be worried if a one quotes the job to take 2-3 days and another says 2 hours unless they explain how or why it will take them less time to complete it; they may have more equipment or a significantly larger crew. Also, I would be concerned if a contractor shows up, asks for other bidders quotes and automatically underbids every other contractor without analyzing the job at hand themselves.
What do their company vehicles/equipment look like and is it well taken care of?
If they don't take care of their equipment, do you think they will take care of your tree and property?
Design and content can give you a sense of their professionalism, as can the appearance of the vehicles they use on jobs. That can give you an idea of how they run their business.
Unless you're removing the trees, demand they not use spikes, which causes unhealthy wounds.
Occupational Safety and Health Administration (OSHA) requires that personal protective equipment be used for any tree care operation. A reputable tree care service will require their workers to be protected.