If you are starting with a big 3 of:
White
Tatum
Giannis
You kind of have the same issue you have now. You need a guard and Pritchard, Hauser, Scheierman, everyone else are not quite starting material, or at least better off the bench. Then you need a big and the same issue with Queta. Unless he makes another huge developmental leap, he is not who you would like staring with this group. So with about $15M to spend, you have to decide, guard or big.
I remain interested in CJ McCollum to add to this group. The idea would be to bring him in a sign and trade. Maybe sign him for over the full MLE (say $20M), trade Hauser in a sign and trade. That only happens if CJM will not commit to ATL. That will use up about $10M of the available $15M, leaving $5M to address other issues, up to $13M if BOS is willing to pay tax (BOS would be hard capped at the first apron).
Another variation on this could be to add a wing, play Tatum as the PF and Giannis as the C. You can do this because Tatum is such a good rebounder. I know everyone assumes that Giannis does not want to play Center, but too bad. You are older now, play center. BOS could use the BAE (about $5M) or part of the MLE to sign a wing to be the 5th starter. Easier to find a wing for that money than a comparable big.
McCollum (S&T for Hauser)
White
Wing-TBD (Sign FA)
Tatum
Giannis