Since you're going to be on active duty away from home for the next six months or so at Basic Military Training and the school for your career field (AFSC), you're not going to be doing any training at a "local" flight school any time soon. Second, once you return from active duty training, you'll be able to check with the benefits counselors at the unit regarding eligibility for various VA and GI Bill programs.
As for working at the unit for more than the minimum drill requirements, that's not going to be an issue until you complete training and come home to the unit. You'll be a full-time, active-duty person for several months receiving full pay and benefits. However, since you'll probably be living in the barracks and eating in the mess hall, if you're smart about things, you should be able to sock away a lot of money during that time, and that will help you get rolling on your flight training when you get home.
Once you do get back to the unit, the opportunity to pick up additional FTP's or "man-days" (or whatever they call it in the politically-correct 21st century) will depend on your specialty (e.g., loadmasters get a lot more days than admin clerks) and your unit's commitments (e.g., only local flying vs getting regular cargo runs to Afghanistan).