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

There is plenty of focus on the downsizing of the troops already, let's provide more accountability in the civilian workforce.  I'm sure there are plenty of good civilians out there, but let's inject some rationality to the hiring and firing process. 

First and foremost we need to revisit the NSS and determine if its the right flavor for US interests and security looking out beyond 2030, we have fallen behind in future tech, R&D, cyber and basic education. Do we really need to prepare for a conventional war against a nation state? (ie; pre-9/11 cold war style) Doubtful... which of the 9 current (and growing) nuke capable nations that we would fight a conventional war against just willingly give up land that we would occupy?.... none... we would have a nuke launched at us before they just gave up sovereign land. The future nation state wars will be fought on/in the cyber and space theater... all non-state irregular adversaries will be fought asymmetrically as we have vs Al Qaeda and the Taliban since 9/11, that means we need a lighter SOF focused ground and air capability for offense and defense for non-state irregular warfare and a robust cyber and space based capability for nation state war. The force needs to be re-aligned and trimmed to provide an affordable, sustainable and realistic capability. Additionally we need to revisit the relevancy of NATO which was built on the premise of the Cold War and the actual utility of the UN. 

Don't try to do more with less.  Don't break a downsizing force with stupid unnecessary tasks. Take stuff off the plate- slow down do the stuff that matters

I believe we are downsizing in the wrong area's of the government.  Downsizing should be in congress and the senate in their pay, perks and medical benefits.  The Military can take care of their own.

How much money are we wasting on civilian contractors that are now doing the work that military personnel used to do? We need to move back toward a self sufficient military that's capable of doing every job that needs to be done.

Develop a system of checks and balances that forces our government to be more accountable by having OTHER Departments (DOT, DOE, NSA, CIA, DHS, EPA) make similar budget and personnel cuts in order to trim the fat. The military is the only agency that will do as it's told because we took an oath to support and defend the Constitution and obey the LAWFUL orders of those appointed over us (i.e. Commanders, NCA, SECDEF, CINC, etc). This does not mean that we check common sense at the door and turn a blind eye to the rest of the world. If we could get entitlement programs, social security, Medicare to somehow shift  more responsibility to the states and less on the federal government, maybe we wouldn't have to pinch pennies on printer paper, toner, and cleaning supplies. The only recourse we have is to try and change things through elections, and it seems every year less and less business gets done. But the cost of living and taxes keep going up. 

Take a hard look at the current promotion system and identify those who truly possess leadership qualities to promote and "cut the fat" on the rest. The current promotion system frustrates talent and puts everyone through the same "meat grinder" instead of singling out & promoting those who have demonstrated they are clearly a cut above their peers.

Anyone that is not deployable (except for those that are on profiles due to surgery, acute illness pregnancy, ect...), have substandard reports, substandard work performances, substandard anything, should be the first to go. The brightest and the greatest should not be the ones leaving.  Train those that are left with viable skills and civilian certification. Cut down on useless programs. Start charging a $5 no show fee for missed medical appointments. Standardize the medical computer systems service wide, both stateside and overseas. The approved system should be utilized by both the military and VA system. Provide electronic medical records. The money wasted on manpower (to include the military, civil service and contract workers) to copy and maintain paper records is astonishing.  STOP changing the uniforms! There should be ONE uniform for deployment to any one location. The money saved here would be astronomical. If the services want to make the uniform unique, do so in the color of the name/service tapes and/or add patches. Very simple to implement. Use the CAC in its fullest capacity: ID card checks (not just those at the gate which use scanning capabilities already), Medical appointment check-in's, Check-in's for any military and/or veteran (VA system) service that requires you to sign in. The redundancies with the sign in system increase's workload and manning requirements. 

Strip out as much non-war fighter spending as possible and remove programs that do not provide defense at all such as the Chaplaincy!