This is more of an advance thread so I do not forget, but with some real talent being added by this regime recently through the draft (3 of the Top 5 Sox Prospects were added in the last two years in Hansen, Pedroia, and Ellsbury).
The Sox have the following picks
27th overall
28th overall (from NY for Damon)
40th overall (supp for Damon)
44th overall (supp for Mueller)
71st overall
83rd overall (from LA for Mueller)
103rd overall
Those numbers may be off, but with 7 picks in the first three rounds, the Sox could get some nice talent out of this.