What we're looking for are positional advantages. Even if Burke is a solid PG, he won't create the kind of mismatch in our favor that Andrew Harrison or Dante Exum create. So drafting one of those guys gives us an immediate opportunity to improve.
Keeping Hayward at the SG already gives us some positional advantage due to his size, strength and passing out on the floor. So to upgrade there, we'd need at least Aaron Harrison or maybe James Young. I wouldn't be in a hurry to draft the kid from Michigan State, for example.
The obvious opportunity for the Jazz is to get an SF, especially given the players in this draft. So I would assume that's still the most straight-forward strategy---Wiggins, Parker, Gordon, Vonleh and anyone else who emerges this year. We could then use our other pick to get a back-up big like Austin or Poythress.
If we don't go with that approach, we might be able to pull off Exum/Harrison with our first pick and a Poythress or TJ Watson with our 2nd pick. We'd come away stacked with this approach too, and can trade Burke or Burks as part of a deal that leverages our cap space and other assets.