Player 1: The draft.
I'd look to get a little more athletic on Defense early on. I really don't have a problem trying to get 2 defensive players in the first 3 rounds. (I assume Finley will be back, but if he isn't our needs will definitely greater on offense)
I'd prefer to add an athletic LB (with the physical attributes of someone like Ezekiel Ansah) who could further complement Clay. Another playmaker may really be the difference maker in making are D amongst the best in the league, I feel.
I'd also like to add another D-linemen, someone in the physical mold of Johnny Jolly / Justin Harrell. Putting aside Harrell's injuries, he had the physical attributes you want on a 3-4 DE: big, long arms, strong, with some ability to get push. A four man rotation on the D-line will help keep all the players fresh and most importantly keep our LBs free to make plays, and hopefully Mike Daniels + Mike Neal are kept in specialist pass-rusher roles to provide some support there.
The only way I'd look to draft a safety early is if there is one that can make a clear cut immediate impact like Harrison Smith did with the Vikings last year. I feel between MD Jennings / Jerron McMillan / Charles Woodson we can squeeze out adequate performance of the S position opposite Burnett.
Player 2: Free Agency.
I would not mind filling one of the positions above - DE/OLB/S - through free agency if we can get the right player on a relatively good contract. First names coming to my mind: Richard Seymour or Laron Landry. The issue with Landry is that I'm not sure you can/should sign him without releasing Woodson. I'm not entirely convinced the Packers are looking to release Woodson.
Here is another scenario: are the Eagles looking to move on from Nnamdi Asomugha by possible releasing him? If so, I wonder if you bring on Nnamdi on a 2 year contract and look to play him at safety. His value will be low, and perhaps he is motivated enough to prove he still has it. If you think he can switch seamlessly to S and still has something left in the tank, I'd think about adding him.
Clearly, I'm of the thought that our defence should be a priority. I think that, outside of LT, there is no pressing need on offense. Maybe at C, but I think EDS showed he is capable enough to at least be an effective enough stop-gap. If you get a chance to draft a LT that you are sure will be able to develop and be a bookend blind side protector for Rodgers, then you jump at that because this team will only go as far as Rodgers' shoulders can carry it. But if you can upgrade the D a moderate amount, I think you've got the makings of a very good Superbowl Contender with the other pieces on offense.
The NFL: Where Greg Jennings Happens.