Vifa, I know where you're coming from, I got out after 10 years, the last 7 overseas and thought I would get picked up by a major airline right out of the gate. 6 months later and after dozens of applications sent, I went to a national pilot job fair where I learned A LOT about the airlines I didn't know.
Number one, it's WHO you know, not WHAT you know, and like a few others have said, unless you know that with internal recs you're going to get a SWA interview, you may not want to get a 73 type. I even met guys at the job fair that told me Delta was going to toss my resume in the can because I wrote "Delta Airlines" instead of "Delta Airline." If you can fly a military plane, you'll be ok in the interview. My best advice to you is to take advantage of what the military can provide to you. Go to Advanced Instrument School, become an instructor, and take the MilComp Flight Instructor Test from the FAA which will give you your CFI. Good luck!