While laws vary from state to state, it's generally required that your teen have at least a learners permit before they can legally hit the road (with a licensed adult in the passenger seat). While they might not need their own insurance if they've only got a permit, it's wise to check with your insurer, just in case, to be sure of your local laws.
Texas is home to the second-highest number of active duty military personnel in the country. USAA caters to both active and retired military service members and their families and holds down 8.1% of the Texas auto insurance market share. Their auto insurance comes with a plethora of discounts — 11 by last count — and you can even save by bundling auto with homeowners or renters insurance. You can also get rideshare coverage through USAA which is an emerging but still uncommon add-on in the current market.
State Farm is the largest insurance company in the U.S. since they insure more cars and homes than any other carrier. In some states, State Farm offers a Steer Clear and Drive Safe & Save programs that offer discounts based on driving habits while helping young drivers learn to drive safely. Check with an agent in your area to see if these options are available.
I am glad to see USAA at the bottom; but it should not be on the list at all. I am currently going through a claim with them (total loss, I got rear ended, pushed into the car in front of me and they hit the car in front of them; not at fault). I have all correspondence recorded and proof of them lying to me, and using made up regulations to justify it. When asked for the reference for said regulations, I am ignored. I have been throwing WAC at them, quote after quote as to how they are being unruly. This was in December, it is now April and they have YET to give me a valuation report in compliance with WAC. I will be more than happy to provide a copy of our correspondence (with PII edited, obviously), proving how bad USAA is at customer service and how willing they are to break the rules if it benefits them. Email me if you want to see it. I finally had enough and contacted the Washington State Insurance Commissioner; USAA has until the middle of this month to respond to them… We will see what happens next.