Assuming our roster at the draft looks very similar, if not eerily the same as it does today, I wouldn't mind going the big route.
I'm confident we won't be resigning Lee so that's one man out of he rotation. I'm beginning to think Sully may not be around either. That said, outside of the obvious choices at the top (Simmons I guess, Ingram definitely), I'd use a late first rounder on Amida Brimah out of UConn. I'm high on this guy for his shot-blocking and ability to finish dunks, something the Celtics are somewhat without excluding 6'9 Amir Johnson. Brimah would bring size and coachability to the roster. A late first rounder may still be a reach for him, but I think he's worth it long-term. Though I'm not entirely confident he'll go into the draft. With the new rules he may declare and workout, but even if he does I don't think he'll be an option for any team on draft night.