With Boozer's Amnesty official and the non-guaranteed contracts waived, it's now certain that the Bulls will be using cap space to sign Gasol and Mirotic. The contracts have still not been announced by the Bulls (let alone compiled on ShamSports) but it's also nearly certain that Kirk Hinrich was signed with the room exception, leaving only the minimum salary exception to sign free agents.
There are other teams out there with space (and exceptions) remaining, so the Bulls are either looking at guys who are passed over, or more optimistically ring-chasers on their last years seeing the wide open Eastern Conference.
In terms of need, I see PG (or at least a combo guard with ballhandling ability) as the biggest spot to fill. The Bulls have 2 players in that role with injury concerns. While we shouldn't plan for an extended Derrick Rose absence, he not only should be on some kind of minutes management but it shouldn't be expected he'll play all 82 games. And while Kirk Hinrich was much more healthy last season than in the one prior, he is turning 34. The Bulls also will undoubtedly give Hinrich a lot of minutes at the SG position (look into your heart, you know it to be true) requiring some spot minutes to be filled at the 1 even when both he and Rose are healthy.
NBA.com has a pretty exhaustive and useable Free Agent tracker, and you can also look at SBNation's rankings from before the signing period (2014 plan got us...#18 on that list!).
Again, we're looking at guys to potentially be signed at the minimum. For instance I would've liked Jerryd Bayless, but he is being signed by the Bucks either through cap space or their own Room Exception. Eric Bledsoe is still trolling for a max offer. Rodney Stuckey will probably get an MLE-level one, Mo Williams a bit less. It'd be great if Jameer Nelson was already thinking of taking a lot less, but he's only getting $2m from the Magic this season and at 32 probably sees this as his last sizable contract.
So...how do any of these guys seem?
Maybe some dude on the Summer League roster, though I'm not really paying attention to that...
Oh man. Thibs has proven to be a wizard at getting value from this type of player, so there's hope that the list will look better in that context. The key is getting someone not to develop but who Thibs would deem reliable enough to not wear down Rose or Hinrich, which probably cuts that list in half. And if you've been meme-ing the Bulls offseason so far, you figure it's gonna be Luke Ridnour. Idaho is sorta the same as Iowa.
There are also low-salaried trade targets, but while the Bulls have a lot of room under the tax to take on more salary, they kind of already used up all their flexibility (yeesh). Butler and Dunleavy are cheap, but current starters. The only trade candidate I see on a moveable, low contract is Tony Snell. And would you deal him for, say, Will Bynum? Probably not.