I would wait until I got settled on the car. If you are going to be in a large college town, or any of the larger Texas towns, public transportation may suit you, at least temporarily. Then you can assess whether you actually need a car for the duration, and take your time shopping for one.
Obtaining car insurance should not be a big deal -- shop for insurance rates (might consider a company where you can talk to a real, local agent, rather than internet); explain that you are a foreign exchange student with a legal driver's license; you have a local address good for the duration; and your rate will be the same as any new 21 year old starting out on their own. Most car insurance policies come in six month increments, renewable.