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

I would have to agree with all who said if they want out, let
them out. Next put the Soldiers back in the positions the civilians are
holding. We spend so much money on these Soldiers; it ends up being a waste.
Next overhaul the recruiting / enlistment and promotion systems. We are at a
point where we can make this a more professional group. Not just by trimming
the fat, but by limiting the crap that is allowed in. Last, don’t make it so
damn difficult to push garbage out of the army. It is easier to involuntarily
separate Soldiers and push them out than it is for someone who failed a UA or
got a DUI.

Sir, I think you pose a good question, but a very broad question.  We are a monstrous machine with a lot of moving parts.  Therefore, there is not a blanket answer for the entire military, or even for a specific branch.  Different levels should focus on different aspects.  With that said, I will throw in my two pennies for some levels(escpecially army). 

The top brass will make or break us (I say us, the warfighter at the tactical levels).  They have some big decisions.  Where will we make our cuts?  How do we determine who gets the axe?  I beleive we can all agree that a major concern regardless of downsizing is the ability to keep quality personnel.  The bottom line is that the military tends to keep those that hack it out and deal with the BS until they hit their 20 years.  Many quality personnel will not stay in because they are not appreciated or they are not challenged, or they are simply a victim of cirumstance.  With the want to decrease numbers even further, we need to ensure that the right people are retained, and the trash is emptied.

At lower echelons, leaders are going to have to continue setting and maintaining standards.  Although nothing matches real battlefield conditions, those with that right shoulder patch need to pass on their experience to some of the new guys that may never know the continued war state we have experienced for the last decade.  This brings me to that lowest level; the junior enlisted.  These are the ones that will have to carry the torch without bottomless pockets that we have experienced during OIF and OEF.  Young leaders and junior soldiers will have to be resourceful and all the time pick the brains of us older folk before we pass that torch.