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

We cannot mortgage future capability for today's emotional concerns.

 In other words, our first priority must be retaining if not a technological advantage at least technological parity with the most dangerous COA enemy. We cannot afford to be technologically superior to our most likely adversary (AQ or similar ideologically based actors), we must retain technological parity with the best force in the world that isnt wearing an American flag on their shoulder. This is not advocating technology because it's cool (F35) or technology that is theater specific (MRAP). From my shallow and poorly placed foxhole, this means cyber defense, targeting affects and delivery, and next generation mobility (regarding mobility, can we please get past the turtle mentality induced by IED's - more armor is not always the answer). We may have to accept personnel reductions to fund the technology we will need to be competitive ten or twenty years from now.

Second priority should be retaining the right Soldiers. Not all Soldiers, just the right ones. Military service is just that - service - not a priviliege and not a jobs program. This is much more difficult because it requires individual accountability from everyone who calls themselves leaders. Policies from on high won't change the culture that allows subpar performers to get promoted. Raters and senior raters who sign good evaluations for subpar performers are at fault. Leaders who fail to counsel are forced to sign good evaulations. Yes, people are people and will always seek out the path of least resistance. I expect more than that from leaders in uniform.

Reversibility and the ability to expand again when needed should be the
focus on this both in terms of personnel, equipment and training. There will
inevitably be another conflict and we will have to expand again, our ability to
do that will be determined by how reversible the changes we make while
downsizing.

When reducing personnel the focus should be on retaining leaders in both the
NCO and Officer ranks as producing those leaders takes a considerable amount of
time. Consideration should be to both low density skills and to the opposite
end of the spectrum to those who have demonstrated that they are more than a
one trick pony (as in a smaller force Soldiers will be expected to become more
generalist and do more things). 1LT Fritz is right in that we need to retain
the right type of people and pay them commiserate to their worth

On the equipping side we must continue to invest in R&D so that we do
not lose technical overmatch, however not necessarily bring every program
through full production. That would mean that we could quickly ramp up
production if needed to fulfill a need in a particular sphere.

Training will necessarily be reduced (and we will return to a tiered
readiness construct to keep some units prepared for contingencies) particularly
in the heavy force but the focus their should be on virtual and constructive
training as we can get them to at least a baseline performance level that could
then be increased through an intensive training rotation if there is a
burgeoning need for heavy forces occurs.