I too flew out of SAT yesterday; the SAT delta counter does have a First/Medallion line. My flight was a 5:55 AM SAT-DFW-FLL that was rescheduled four times since Wednesday. SAT-DFW left about 45 min. late and I missed my connection to FLL, the choice was to wait at DFW for five hours for the next FLL flight or change to a PBI flight leaving right away. I took the PBI flight and arrived with no problems. The only problem was my checked bag never made it; Delta just delivered it to the motel 10 min. ago.
The biggest problem I saw yesterday was getting flight crews to the aircraft before the flight. Both of my flights were delayed due to late arriving flight crews. All in all Delta seems to be doing a good job of getting their flights back in operation.
My airport experience was not too difficult, with the only difference, having to show ID and ticket at the security screens. My laptop was not searched, but I did take the time to check anything that I thought would looked pointed. Place all small screwdrivers and knifes in you checked baggage and you should be fine. Lines are extremely long; if you are Medallion or traveling First Class find those check-in points for somewhat shorter lines. Persistence and patience pays off in contacting Delta, and a good redial button on your phone will be needed.