I think the Ball Handler / Wing positions are pretty easy to work out, with three guys for each:
Ball Handlers: Smart, Thomas, Turner
Wings: Bradley, Crowder, Jerebko
That leaves four spots in the 'big' positions.
Firstly, I think Olynyk and Johnson are locked in since both offer a very valuable set of skills that no other big on the team can match:
Olynyk
Olynyk is a legitimate outside threat, who opponents must respect from three-point range. He's also a very good footwork and ball handling for a big, so if the defense runs hard at him to challenge the shot, he can put the ball on the floor and drive to the basket. When he gets to the basket he is a very good finisher (67% FG inside 3 feet) which means the defense must respect not only his shot, but also his drive. If he is trapped or double teamed then he's got the court vision and passing ability to find an open teammate, and if he's fouled he is a solid free throw shooter. Olynyk is also an good offensive rebounder (3.0 Off Reb Per-36) which he rarely gets credit for. All of this combined makes him a tougher cover than people realise, especially as a 7-footer. He's easily the most offensively versatile big on our roster, and the only thing that really holds him back is foul trouble (around 6 fouls Per-36) which limits his potential playing time. Until he works out how to play D without fouling, he will most likely be limited to a bench role.
Johnson
Johnson is a unique player for us because he is effective at both protecting the rim and defending the perimeter. He is capable of challenging shots around the basket (career 1.7 Blk Per-36) and is also capable of pulling in the rebound (career 9.1 Reb Per-36) to finish the possession. On the other end of the court he is capable of getting a lot of second chance points since he is an excellent offensive rebound (career 3.4 Off Reb Per-36) and finisher (career 70% FG inside 3 feet). Johnson is basically the perfect "scrap guy" because he is a guy who can impact the game on both ends of the floor without ever needing a play called for him. His defensive versatility basically means he is (to our defense) what Olynyk is to our offense.
So, that leaves Zeller, Lee and Sully fighting for the final two 'big' spots.
Personally, I'd take Zeller first. Out of these three guys he is the tallest, the most mobile, the most defensively versatile (not like that's saying much) and the most offensively efficient.
That leaves Lee and Sully who, on the surface, appear to be very similar players. I'd like to tell myself this is a hard decision, but sadly that's not the case at all.
Lee offers the following advantages over Sully:
1) Significantly better finisher around the basket - 67% vs 62% inside 3 ft)
2) Far more efficient scorer - 1.24 vs 1.09 Points Per FGA
3) Decent mobility and ball handling - can drive to the basket (unlike Sully)
4) Superior conditioning - allows him to bring more consistent effort and reduces injury risk
5) Far superior at drawing fouls - Career 33% Free Throw Rate, vs 18% for Sully)
6) Veteran leadership - He has both "All-Star" and "NBA Champion" on his resume
7) Better attitude - Doesn't have Sully's poor shot selection, or his tendency to attract technicals
Sully offers the following advantages over Lee:
1) Three-point range (albeit too poor a percentage for it to be a major advantage)
2) Youth (a moot point if he signs elsewhere in FA)
I'm going to say that Lee wins this one pretty comfortably, so with all that established my rotation would be something like:
PG: Smart (28 min) / (28 min) Thomas
SG: Bradley (28 min) / (12 min) Turner
SF: Crowder (25 min) / (23 min) Jerebko
PF: Johnson (24 min) / (24 min) Lee
C: Zeller (26 min) / (22 min) Olynyk
That leaves the 'emergency backup' rotation of:
Sully
Rozier
Hunter
Mickey
Young/Jones