Note: I will add periodic updates throughout Monday as new information comes in.
I'll call this the "final" first-round projection, but I'm hoping to update this throughout the day on Monday. Many high-level sources are telling me they're not finalizing the tops of their boards until Monday morning after they better establish signability on the players in their mix. As of Monday morning, here's my best estimate of the first round -- as always, based on information from industry sources.

Pittsburgh Pirates
Gerrit Cole, RHP, UCLA
I know they did their due diligence on several alternatives here, but Cole appears to be the choice.

Seattle Mariners
Anthony Rendon, 3B, Rice
Although I've heard Bubba Starling here as well as Francisco Lindor, individual sources and overall industry consensus have them on Rendon. Starling is a favorite of GM Jack Zduriencik, though.

Arizona Diamondbacks
Trevor Bauer, RHP, UCLA
This seems solid now after they looked at a number of options, including Dylan Bundy and Archie Bradley.

Baltimore Orioles
Archie Bradley, RHP, Broken Arrow HS (Okla.)
Could still be Danny Hultzen here, but late word has them working on Bradley after Hultzen's big contract demand came out.

Kansas City Royals
Dylan Bundy, RHP, Owasso (Okla.) HS
They want a polished pitcher who'll move quickly through their system, and Bundy fits. I've had two evaluators call Bundy the best player in the draft, which would be quite a coup for a team picking fifth.