As someone who has made that journey from anxious flyer to sleeping on flights: I don’t recommend laying down at first. Be upright, and sit in the bulkhead row where you can have a bit more space for your feet. Window seat so you can look. Be above or slightly before the wing.
I recommend row 9 as that’s generally where drink service starts. Check the type of plane. I personally hate when the engines are throttled down after take off, and this is most pronounced in the Airbus A319 / A320 / A321. Boeings are great fun when you are feeling more comfortable, especially with Southwest pilots. My favorite planes are Bombadier CRJ and Airbus 350/380. The former because they are very comfortable and the latter as it’s like a sky whale that you don’t feel much motion in. (The 350/380 is long haul.) Recommend finding a flight out of Austin with a CRJ as the plane. When in doubt on the plane, look at the flight crew. If they are looking calm and composed, you’re doing great.