There are a lot of threads for draft and trades and so on, but it seemed like there should be one for the off season overall.

The main discussion will probably be around caps and aprons and how to build the roster.  Spotrac has BOS active salary at $187,730,180.  This is the sum of the currently signed 14 active players and does not include anything for Vucevic or added rookies:

Tax Room              $13,269,820
1st Apron Room     $21,269,820
2nd Apron Room    $34,269,820

This includes all of Walsh, Williams, Shugla, Harper, and Banton.  The 14 current roster players plus 1 draft pick would put it at 15.  I expect 2 of those will not make the team and that Vucevic or someone like him will be added allowing BOS starts the season with 14 on the roster.  So if you subtract out Banton and Shugla, add in the salary for a #27 pick, here is where BOS is at with 13 roster spots:

Tax Room             $15,922,083
1st Apron Room    $23,922,083
2nd Apron Room   $36,922,083

By my math (which is usually off to some degree) that means BOS could realistically spend around $10M-$15M on that last roster spot, barring other moves, and stay under the tax.  If you trade Hauser (as has been discussed) and replace him with a min contract, that would free up an additional $7M or so giving BOS $17M to $22M to spend under the tax.

I think the most that BOS could spend would be the NTMLE which I think is about $16.1, although they do have a large TPE if they want to spend more (using the TPE would hard cap them at the first apron, as would using the NTMLE).  I think that some good players will be happy to get the full NTMLE, but there are not that many interesting FAs available this off season.  CJ McCollum maybe?