If I can choose three I'd keep Bougans, Wallace and Humphries.
Bougans because:
This is a young team that could really use a veteran role model who who is a little more grounded than Rondo.
Secondly because he has a proven history as a solid 3+d player, which we could use. That's a role Lee was supposed to fill until he proved himself mediocre at both 3 and D.
Wallace because:
Without him we don't have any legit SF to back up Jeff Green.
Wallace has the combination of strength, atleticism and toughness to guard just about anybody on the floor. That's a very valuable asset to have if you play a defense that involves a lot of switching as Boston tends to.
Secondly he has no pressure on him at all. Zero expectations. Only two seasons back he averaged 15 points, 7 rebounds, 3 assists per game for the Nets - similar to what he has produced for the past 10 years. Since his struggles last year everybody is writing him off as being done, like he is nothing more than a trade asset (i.e. contract) with nothing left in the tank. His rep cannot really fall much lower so he has nothing to lose, plenty to prove and everything to gain. If he comes even close to what he produced only two seasons back, it could be a serious game changer for these Celtics.
Humphries because:
This team has sucked at rebounding since the big 3 era began, especially offensive rebounding.
Humphries has a career average of 11 rebounds per 36 min (3.6 OFF) and his REB% numbers are consistently towards the top of the league rankings - he has proven that he is one of the better rebounders in the NBA.
Bass and Olynyk are both pretty average rebounders, and Sully is a question mark due to his health and Domestic Violence charges. Until he is cleared of both issues, Hump is the only quality rebounder we have. Even when Sully does return he's still going to need help on the boards, and right now Hump is the only guy qualified for that role.
Secondly Hump has averaged 1.2 blocks per 36 min over his career, so right now he is probably the closest thing to a shot-blocker we have on this roster. Without him opponents will score in the paint at will. With him they probably still will, but he may at least help a little.
Hump also averages 3 FT made per 36 min which is decent enough. He'll aggressively crash the boards so he'll get his share of garbage points off putbacks and free throws - he won't need plays called for him to get his name on the box score.
If I have to choose two of those guys I will keep Wallace and Hump, but I don't mind Bougans too.
Hump would have to be the guy we need most out of that group, but he's also the only one with any real trade value. Still we don't need to trade him just because we can. I'd rather make use of his skills (which we desperately need) and then just let the $12M come off the books next season, possibly re-sign him on the cheap or use that cash to sign a free agent (or both).