Great question by the OP. Here are the traits I think will be necessary.
- Relentless pressure on D. Ability to switch defensive assignments all over the floor. Great team defenders who talk and share responsibilities.
- Lots of multi-talented guys with size. To play the defense already mentioned, but also to be able to do everything -- rebound, start the fast break, finish at the rim, handle the ball, shoot the 3, etc.
- A dominant big man built for the modern NBA. That is, someone who can punish you down low, handle the ball, pass and shoot on offense, but move his feet on the perimeter on defense. There are hardly any of these guys out there in the league right now (Anthony Davis, Karl Anthony Towns, Joel Embiid), but there might be a few on their way who are currently teenagers.
- Great coaching and team basketball. This isn't just about superstars, it's about a team-oriented culture, guys who play together rather than trying to play hero ball, and a great coaching. It takes time to gel like that, just as it took time for the Warriors to become the team they are today.
Can the Celtics get there? I think they're building the culture and they've got the coach. But the players?
- Fultz may be that multi-talented guy at the 1-2 position. Has size and length to switch and defend on D, can shoot, rebound, handle, pass. Good instincts in the pick and roll. Gotta draft this kid and see what he becomes.
- Jaylen Brown and Marcus Smart could be very important. Guys that can do everything on both sides of the floor. Gotta have patience to see how these guys develop, especially in Brown's case.
- Not sure about a dominant big. I don't think Zizic is likely to evolve into that guy, though he can play an important role. Apparently there are some really intriguing do-everything bigs coming out in the 2018 draft, which would argue for the Celtics to be careful trading that pick away.