Under this scenario I'd hate to have the #1 pick.
There is one aspect that can't be underestimated when being picked #1; how will they hold up under the pressure? Over the years many of the #1 picks have talked about the tremendous pressure they are under to live up to the enormous expectations that the positions garners. Stars can handle it, role players simply can't survive under that weight.
https://bleacherreport.com/articles...f-nba-draft-is-an-honor-and-often-a-curse-too
So when considering who I'd take, and since the OP has eliminated the tantalizing potential of a trade, I would have to consider who could handle the pressure of being taken #1.
I see Deni, Obi, and Onyeka as strictly complimentary pieces. And even though I like them, I don't see how they could possibly survive as the #1. Tyrese and Killian offer too many uncertainties for me to be comfortable taking them that early. James Wiseman already has questions about his heart and love for the game, reminiscent of Olowakandi, so I'd back away from him.
That only leaves Anthony and Melo. Both have a swagger to them that fits the mold of the #1 pick. Melo has been groomed to be in the spotlight through his family, and Edwards already thinks he's the best player on the planet. Do they have MAJOR flaws? Yes. But they pass the confidence test.
Edwards just doesn't fit here next to Book. At best he'd be a great player to bring off the bench, but I can't see his ego surviving long as the backup SG.
Therefore, I lean Melo. On top of his skill sets we've talked about ad nauseum before, he's flashy and will attract attention through highlight reels. Normally I wouldn't care about that, but it will keep his stock high so we wouldn't lose value on a future trade. I see him in the Ben Simmons mold with better handles and FAR more confidence shooting (even though he's terrible at it). Melo could very well be a flashier Ricky Rubio.