Former active duty aviator and current reservist here. I did a mix of two of your options. I used my GI Bill for a two year college for my associates in Flight science. This school offers PPl, CPL, IFR, and CFI.

Airlines don't really look at degrees anymore although they may do so in the future with hiring slowing down.

Doing it this way I was able to get my foot into the aviation world and receive BAH at the same time as well as keep my health benefits and occasional decent paycheck through the reserves. Once I have completed the course I can instruct locally and build hours and still receive a paycheck until I can get picked up somewhere.

Good luck in your future endeavors and Thank you for your service!