I agree on the "get a degree in something useful" department. Having the option to work outside the field (pilots on average get laid off at least once, I know a guy who has been laid off 6 different times [more than normal by a long shot])
The only useful thing about the aviation degree is the chance to land an internship with an airline and make contacts for the time when you can finally get hired to fly. Everybody will have hours when you get to the interview; so knowing people and having letters of rec. or having your application "walked in" by a contact can sometimes mean the difference between getting the interview or not.
(If you get the interview, they've already decided that they WANT to hire you, just don't give them any reason to think otherwise and you'll probably get the gig.)
You have to spend your own money to get your private pilot's license, but instrument-MEI can be paid for via VA funds, so make sure you have 4-6k put away for the private....I recommend AF or Navy flying clubs for the best prices....Also, only certain flight schools are eligible to be used for VA funded training, make sure the one you want to use qualifies.....Some of the on-base flying clubs have that capability, some don't, but I still suggest using them for your private.
Good luck, and thanks for your service.