I live in Stafford. there is a standing F-calss match monthly at Quantico. I forget the web site for it. I will ask a few friends and see if they have it.
As far as QSC your shoot at the mercy of the USMC (Of Course) if there is no RSO there is no shooting.
You do get to use ranges out to 600m (762 and under ONLY).
I belong to a club just off post that has a 100 yard range. HTTP://www.iwla.us/
Other than these not much else around for shooting.
Being Active Duty you get a good rate on the QSC and I would go for it. For you it would be well worth the money to join it.