What's the most important thing the military should do while going through this downsizing period?

I would agree with eliminating some of those items.  I rarely go to the PX unless I have to go or unless I am looking at their clearance items.  I would like to see that go to contracting and have companies bid to provide these services to a captive audience.  It amazes me that I can go off base in some locations and get gas, haircuts and other items cheaper.  One example would be the barbershop, in the last year the cost of a haircut at my location went up 10%.  However, I did not receive a 10% pay raise.  When I asked about this I was told they do a survey of the surrounding area and keep the price within a percentage range of the average.  I do not really find that as an acceptable answer as elements on the installation do not have all of the same costs of doing business as off post businesses have.  The same applies to fuel!

I also think we could reevaluate all of our MWR activities and determine which activities are better managed by civilian elements.  For example, and this may not apply to all installations, I have been places where it costs more to bowl on base than it does off base. 

BLUF:  If there is a service on the installation that does not enhance the lives of our Soldiers and Families AND it is more costly than receiving that service off base, we need to evaluate whether or not we need to keep it.

I do not believe there is any one "most important thing".  Below are my top 6 (in no particular order):

1. I think we really need to assess what it is that we want from our Soldiers when we go to war.  If we are going to contract cooks, maintenance personnel and other positions, then we really do not need them in the Army.  I would start there. 

2. Reevaluate those tasks that we do in Garrison that do not support our combat mission.  If it does not bring value to the Army then we stop doing it.  No more pet projects.

3. Evaluate the like tasks that are accomplished across all branches of services.  Decide which branch would be best to manage those tasks and assign all those personnel to that branch for management.  (If medical is assumed by the Army then all medical personnel will belong to the Army; if all fight activities are assumed by the Air Force then transfer ALL those activities to the AF; if all HR activities are assumed by the Navy then all HR personnel would be assigned to the Navy).  The 2nd and 3rd order effects of this would amount to phenomenal savings to the DoD. (I could go way more in depth on this)

4. Consolidate installations across the DoD.  I have not seen any conflict that we have fought since Vietnam (and probably further back) that only involved one branch of the service.  There have been separate missions; however, those support the larger goal.  This way we are actually working with the other branches before we go to war (or peacekeeping missions). (I could expand on this as well)

5. Consolidate the entire education system in the DoD.  I am amazed at how fragmented we are across the board when it comes to education.  A simple restructure to mirror a University system would eliminate much of the redundancy that occurs across the branches.  This could be done just in the Army; however, the gains would be amazing if we incorporated the entire DoD.  Once again the 2nd and 3rd order effects would be unbelievable. 

6. Get out of the real estate business!  We started this when we privatized family housing, we need to take it one step further and privatize the barracks as well.

Not give all recruiters new Android Galaxy S4 phones with unlimited data text and minutes.... Not the best way to blow a broken budget.