Arrival at AUS is a dream. After strolling some corridors and avoiding the temptation to skip past the tensa barriers to the street you end up in a one belt baggage claim. On the left are the APC booths and the GE on the right, which you can get out of the way while waiting for any luggage to show. You can clear extremely quickly as the combined immigration and customs desks are only for the BA flight (although i hear Lufthansa may start doing flights soon too which could interfere?)
The airport is very close to the city so there is no need to build in much journey time before your return, unless you are very keen to spend time on the putting green in the club. I found the staff in the club to have great southern hospitality, with table service in the bar area and they generally "forgot" to take the vouchers for many of the premium drinks.
Enjoy Texas!