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Then thats a good problem to have. If I had an offer from the airlines you mentioned, for me, it would be a no brainer: Delta.What if you get a job offer from more than one airline?
Eastern, TWA, Braniff, Pan Am. Pan Am is launch customer for 747, so that would be a cool place to be. All are established companies with international flying. "Proven" companies.
I repeat, Southwest, that outfit called "Federal Express" (flying Falcons to carry mail !), and that freight company United Parcel Service (they have those brown trucks) is looking at buying some planes to "try out" air freight (which won't work,thats why we have the MAIL - duh).
Stay away from those. You might be the first pilots hired in their history but it won't last and your retirement won't compare to big Pan Am.
I would use them as "stepping stones", maybe try out the airline world at SWA for a couple years but I would focus all my efforts into sliding over to TWA or Pan Am, they dominant the 747, L-1011, etc international arena and your career earnings and job stability will be much better off.
Also stay away from federal government jobs. Your income is "fixed" and retirement will always be X. FAA Flight Inspection, US Customs, etc are rumored to be hiring big time soon but keep your eye on the goal of AIRLINE PILOT. Pass on those jobs and interviews, you will just get side-tracked. You invested a lot in your training, go to the place it will be rewarded. That is the big iron-international carrier.
If you need further info, go to the library and read some of the books by DARBY, KIT. That will get you started.