This is a longer form of what I've been saying in various threads.
If the next CBA looks a lot like the current one, the Celtics will be able to add, at most, two guys making more than the minimum (or slightly more, if they give their non-Bird free agents the raise they are allowed to give). If the next CBA looks more like the owners' draconian hard salary cap proposal, the Celtics are probably not going to have room for anything more than bargain basement free agents.
Either way, if the Celtics want to add youth and athleticism to the team, they're going to have to do it on the cheap. NBA veterans who can be had for the minimum include declining has-beens trying to hang on, never-was journeymen who are career bench players, injured guys looking to bounce back, and failed prospects. The later category, especially when you can say the player was misused or irrationally in a coach's doghouse would be the best shot at looking for younger, more athletic players.
Another place to look is the D-League. Austin Ainge in his new front office job may be able to point out players he coached against. Maybe dreams of Tiny Gallon were burst when Maine traded him to Bakersfield for a draft pick, but maybe you want to think about the guy he was traded to create room for, the familiar Stephane Lasme. Two big men who intrigue me are Sean Williams, a former Nets first round pick with off-court problems who was runner-up to Chris Johnson as D-League Defensive Player of the Year, and former D-League MVP Courtney Sims, who seems to consistently be [dang]ed with the faint praise of being one of the top bigs in the D-League. You probably won't find a future All-Star, but you might find the next CJ Watson or Von Wafer, two name to guys who spent time down there without being assigned by an NBA club. Atlanta grabbed Magnum Rolle at the end of the season to get a head start with him, just as a healthier Celtics big man rotation probably would have led Ainge to hang onto Chris Johnson (who the Blazers seem to have signed through next season).
There are draft picks, and I am sure we will be debating those pretty soon.
And of course there are undrafted free agents. Ben Uzoh, Wesley Matthews, Marquis Daniels, and Reggie Evans are some recent players to succeed despite not being drafted. Some players in this category may have spent time overseas before returning to the US.
It's difficult to speculate about trades and free agent signings without knowing what the rules will be in the new CBA, but regardless of what happens in labor negotiations, these are the sort of players the Celtics could and should be looking at and a better choice than looking at broken-down veterans to back up an aged core.
If we're going to speculate about what Boston can do to replenish the bench, we might as well think about things that might actually happen. Danny Ainge probably doesn't read this board, but you never know....