I can only speak for the Air Force. But the other service are probably the same.
You need to join and go thru USAF Pilot Training, about 13 months. You can select to be a FAIP, First Assignment Instructor Pilot, in the T-37, T-6. I don't know about FAIPing to the T-1,T-38. You could when I went through, 1995, but times have changed.
Talk to a recruiter. Better yet try getting a slot in the Air National Guard or Air Force Reserves. Your life will be better and you can still have a civilian career. Call your local ANG unit to find out if they are having a pilot interview board anytime soon.
They still have T-1 and T-38 FAIPs. As a T-38 FAIP, I'm living proof.
FlynChick, be advised that there are no certainties about your assignment. Although you can let it be known that you want to be a FAIP, you could get sent anywhere, and to almost any airframe. USAF pilots also incurr a 10 year active duty service committment on the day they get "winged," so keep that in your crosscheck when making the decision.