With Derrick Rose (or Beasley, of course) coming into the fold, it truly changes the dynamic of how this roster will be assessed.
Rose will be 20 years old by the time the season starts, and I think age is both an easy and useful way to group the roster once you get beyond the castoffs and contract filler (Duhon, Simmons, Brown, Nichols, Curry...maybe Gray):
Tyrus Thomas: 22
Luol Deng: 23
Joakim Noah: 23
Aaron Gray: 23
Thabo Sefolosha: 24
Ben Gordon: 25
Drew Gooden: 27
Kirk Hinrich: 27
Andres Nocioni: 28
Larry Hughes: 29
Separating the roster that way is biased and somewhat arbitrary, but it also coincides with the general consensus of when NBA players are either before or at their prime.
I'm not suggesting that Aaron Gray is more valuable than Drew Gooden because he's younger. However I do think that Paxson needs to think in terms of age relative to Rose (or Michael Beasley, of course!). Merely adding a top-flight talent to the roster (and a coach that doesn't hate that roster) will work wonders, but the goal is to get a championship contender together when Rose (or....forget it: Rose.) is ready to lead them to that title. The old idea of 'the core' should be gone, with a new one forged from that first group of players, yet to hit their prime.
That long-term outlook can be tied into the more immediate goal of eliminating some roster glut, a problem that existed even before the lottery was won. I'm not suggesting getting rid of everyone at their prime (pretty nice to have nobody past it, I must say) for picks and cap space. This team is young enough already and teams do need veterans. But when Paxson is, smartly, exploring a trade to consolidate talent, those in the second group should be the ones moved, even if it's only to free up roster space, salary, and minutes. The Bulls can take in-prime talent back, as long as it's a result of fewer bodies with fewer contract years.
As always, if it's a deal for an upgrade, those yet to have hit their prime are then also in play (starting with Gray and Thabo, and work up from there). But beyond picking the right guy (Rose!) at #1, Paxson has work to do with this roster. There's too many players who need minutes and money. And as a side benefit, any shuffling of the deck further distances the franchise from last season.