I would lean toward a 50cc Honda Ruckus, but they don't appear on the "Approved" list for some reason... There are some Ruckus owners here, so maybe one can explain why. It may be capable of >30 mph
Unfortunately, you do have to have a vehicle operator's license to operate an unlicensed scooter in Texas...
For precision, the scooter doesn't need a license, but the operator does. At 15, one can obtain a moped license.