Given the major minute restrictions on all players, I thought it would be nice to see the Per-36 Minute numbers for each of the players.
I couldn't easily find such a list online for preseason stats, so I threw numbers into a spreadsheet and calculated it myself!
Thought I would post it here for everybody's entertainment:

The guys who stand out to me:
Avery Bradley
19.1 pts, 5.6 reb, 3.3 ast, 3.3 stl, 47% FG, 52% 3PT, 100% FT
Amir Johnson
20.1 pts, 10.2 reb, 1.6 ast, 1.6 stl, 2 blk, 60% FG, 50% 3PT
Jae Crowder
15.2 pts, 7.3 reb, 4.2 ast, 1.8 stl, 54% FG, 56% 3PT
Jordan Mickey
21.2 pts, 11.1 reb, 1.0 ast, 1.6 stl, 4.2 blk, 56% FGTerry Rozier
19.0 pts, 4.2 reb, 5.4 ast, 2.7 stl, 49% FG, 57% 3PTJared Sullinger
17.7 pts, 15.4 reb, 4.6 ast, 1.3 stl, 1.9 blk
Isaiah Thomas
21.5 pts, 3.7 reb, 8.3 ast, 1.5 stl
Tyler Zeller
20.0 pts, 8.5 reb, 2.0 ast, 0.7stl, 1.7 blk, 65% FG, 85% FT
I will be keeping a close eye on the highlighted ones!

Also worth noting that Boston finished the preseason with a 6-1 (85.7%) win record. This puts them at the equal second best record in the league, behind Charlotte (7-1, 87.5%) and tied with Memphis.
Lets hope this is a good sign, and that at least some of this success will project into the regular season!
Note
I only included players who have a shot of being with the team when the regular season starts, so the red-claw certainties aren't on here.