I am going to assume that the Brooklyn Nets do not move out of the 18th spot in the draft and will therefore end up giving the Celtics that 18th pick in the draft. So given that, if the Celtics win the lottery I think they choose Wiggins as I think Danny would have Wiggins at the top of his draft board. The upside potential of Wiggins is the highest in the class.
If the Celtics select Wiggins I would expect them to trade the second 1st rounder possibly with Jeff Green for a center. Yes I am thinking Houston sending Asik, possibly in a three way. Just seems that with a very good chance of Wiggins being able to give this team as much if not more than Green, it makes sense to move Green and the pick to assure a rim protecting center and assuring Sullinger gets switched to his natural PF position. A Rondo-Bradley-Wiggins-Sully-Asik starting rotation could be very good and probably the team would be more willing to get that center than care about losing a redundant piece in Green and a mid first that might require another young player needing development when you already have Sully, KO, Wiggins, Faverani, and possibly Johnson and/or Pressey, though I am very pessimistic on those two being on the team next year.
Selecting 2nd and 3rd is a bit more complex because it depends on who was off the board at #1 and who is left. If you can still land Wiggins over anyone else while selecting 2nd or 3rd then you do it and probably still trade the 18th pick. If Wiggins is gone then I believe Embiid has to be the pick. I trust Parker to be able to be more sooner and be able to contribute as early as next year offensively but I think Embiid's potential and physical stature and natural athleticism makes him the higher upside of the 2 at a position of greatest need on this team. That I think makes Embiid the pick at 2 and since the C's are going to bring along Embiid slow, with the 18th pick I think they take who is left of Garry Harris, Nik Stauskas, TJ Warren and Rodney Hood. All these players I think the Celtics could utilize next year in the rotation much like Olynyk has been this year and Sully the year before while Embiid is brought along more slowly.
Selcting 3rd, if the Celtics win that slot, I think means taking whoever is left of the top three players: Embiid, Wiggins, Parker. Having already looked at the scenarios of selecting Embiid and Wiggins then lets assume at the 3rd pick Wiggins and Embiid are gone and so the Celtics take Parker. That probably means Jeff Green is gone and I could see a scenario playing out where the C's move Green and the pick for Asik again. But I could also see selecting Parker and then taking a shot at Cauley-Stein at pick 18. If he is unavailable I could see the Celtics looking to grab a shooter and moving the 18th pick up or down to grab a shooter like Stauskas, Bogdanovic or Hairston to compliment the Bradley/Rondo backcourt.
Selecting later I believe the Celtics have to take BPA. I value Tyler Ennis more highly than some and think after the top 3 he might be the best player in this class in a few years. But selecting him is problematic because the Celtics have Rondo. Does Danny take BPA whether that be Ennis or Smart, when the best player you already have and have spent a year installing as the face of your franchise, is Rondo? If so Rondo will have to go, eventually. But it also means needing to keep your 18th pick and try to land another player to add to mix somewhere else because you just drafted your backup plan at PG high in the draft so now you have to hit again with the second pick. Here is where I think Ainge could raft on potential and guys like Jerami Grant, Clint Capela, and Dario Saric come into the thinking.
Hoping for the best of the best but even looking at all the various scenarios that could happen, if you like young talent and seeing it develop, you are probably going to love watching this team next year, when they will absolutely suck once again but the young guys should be growing.