If we're looking at free agents, these are the top center candidates that I can quickly think of:
Dwight Howard (6'10"; 36 yo)
Hassan Whiteside (7'0"; 33 yo)
Lamarcus Aldridge (6'11"; 37 yo)
Damarcus Cousins (6'10"; 32 yo)
In terms of some superlatives, I'd say:
Best defender, overall: This is close, between Howard and Whiteside. I'd lean toward Howard overall in terms of defense.
Best rim protector: Whiteside
Best defender in space / best on switches: None
Best passer: Cousins
Best 3PT shooter: Cousins
Best finisher at rim: Tie, Whiteside / Howard
Best mid-range: Aldridge
Best rebounder: Whiteside, but very close with Howard
Overall, I don't think Aldridge makes a ton of sense unless it's for the deep bench. As a primary backup center (and now, starting center) I'd want one of the other three.
All three of Whiteside, Howard and Cousins will bring good rebounding. The question is, do we prioritize rim-defense and finishing around the basket, or passing and floor stretching?
And, if we are looking for shot-blocking and lobs on offense, what makes Howard a better fit than Whiteside?