Comparing military aeroclubs' rates to "downtown" rates is like comparing apples to onions--the only thing in common is that both are spherical. Although it was eons ago, and the prices will shock you, when I learned to fly at the EDF Aeroclub in 1972-3, if memory serves, 150s went for $11/hour and 172s went for $13. At Merrill, typical 150s went for $22 and 172s were $27. Instructors at EDF were paid $5 or $6, and downtown it was $12-15.
Incidentally the EDF club was a 141 school; I have no idea whether VA benefits could be used there. When I got out and started using my VA benefits, it was at a part 61 school in Laramie, where I later worked as a part-time instructor and SE charter pilot.
Sometimes the choices of schools are dictated by the limited offerings within a reasonable distance. For instance, there was only one plus the UW flying club in Laramie, which at the time was only open to UW staff and students. The nearest alternative schools were in Cheyenne (50 miles) or Fort Collins (65 miles).
Cheyenne's was VA-approved, but they ran it like they didn't care at all about their students--which is why I never got my ME. I went there for my first ME lesson--"Sorry, your instructor had to take a charter." Made down payment anyway, then reschedule, drive over the hill again, same story. Reschedule again, drive over the hill again, same story--this time I told them to give me my money back and cancel the program. First I was told that they never refunded down payments, but I'd have to reschedule again. I insisted on seeing the manager. When he balked but finally said he'd mail me a check the next week or two, I told him either I got my money back right then or I'd be suing them tomorrow. He went into his office and wrote me a check.
But if there are several choices in the area, check them all out. Ask questions, listen to the answers, look at their equipment, compare prices--not totals, but per hour, because totals mean nothing unless they add the caveat that everyone learns at his/her own pace. But don't compare their prices to a military aeroclub, because you're back to the apples/onions issue.
Cary