Wiggins
I don't think Parker (not talented enough) or Embiid (back issues) will challenge Wiggins for #1 ... but I think Exum might have a shot.
Exum looked really good in that Nike Hoop Summit game. The speed, the explosive athleticism, size, ball-handling, can get to the basket and has a decent jump-shot. Has the tools to be a strong defender/rebounder and played PG so should have good passing. I know hardly anything about Exum outside of that one game but the team have obviously been watching a lot of him and, if those scout trips have been positive, I could see Ainge rolling the dice on Exum over Wiggins due to Wiggins' inconsistency / passive behaviour.
So I think there is a good shot Exum would be Wiggins' toughest challenger for that #1 spot if Boston get the #1 pick. Not Parker or Embiid. But Exum.
If Danny targets Exum as his top pick, golden opportunity to trade down to 3 or 4 and maybe get another lottery pick in the process, or at least an extra first round pick.
I agree, and will take it 1 step further:
If Ainge would be happy with either of Embiid, Wiggins, Parker or Exum and he gets the #1 pick, he goes to either Philly, Magic, Jazz, all who have 2 first rounders, and trades the first for their two firsts, as long as their top pick is in the top 4.
Philly also has 3-4 second founders this year too.
Lots of possibilities.