What to look for - bringing an aircraft back to life

I seek the collective wisdom of the group. As I have mentioned previously, I
was the co-owner of a 1965 Piper Aztec, due to various conflicts in the
partnership, the plane has not flown in two and a half years (approx.) most
of this time it has been in a heated hangar, but has been out in the weather
since April. I have just this past week convinced my partners that it was
doing no one any good to have it just sit there, and they finally let me buy
them out. It's a pretty decent airframe overall, it's just been sitting idle
with disuse. I know there are many things to get it airworthy again, and
have started the process. I have scheduled a pitot-static-transponder check
this coming week, and an annual will shortly follow. I intend to replace the
tires (figure they're probably rotted due to not being moved much, and it's
a easy thing to correct right at the start), install a new battery (and if
memory serves I'll need to check/replace the one in the ELT as well). My
question is, what else should I be checking extra carefully? I know the
annual should catch most things, but that's just an inspection by
definition, and I expect not everything will show up until I get it flying
again. The engines have been run occasionally, but nothing that I'd call
consistent. The engines do have chrome cylinders, so I'm hoping that I won't
be facing a horrendous corrosion problem in that area. I'm wondering what
things I should be extra careful/mindful of once the airplane is airworthy
and flying again. Where would I expect to see problems the first few hours
aloft? Should I keep it close to home for the first bit and then do some
longer cross countries to give it a proper shakeout? If so, what would be a
reasonable amount of time to shake things out? The aircraft and I are based
at Jeffco (KBJC) in Broomfield, CO. I am really looking forward to taking a
flight in this aircraft, as I've owned half of it for 2.5 years and have
never flown it. I've seen those in the group who have been, or are in
partnerships, however the whole mess surrounding this one has made such an
idea in the future somewhat unpalatable.

--
Louis L. Perley III
N46000 - C152
N370 - PA-23-250