Correa said he'd like to stay at shortstop, and he plans to use his signing bonus to help his family financially. The Santa Isabel native starred at the Puerto Rico Baseball Academy and is committed to the University of Miami, but is likely headed to Houston's farm system instead.
With the second pick, Minnesota took speedy Georgia high school outfielder Byron Buxton, considered a five-tool player with a bat considered the best among all draft prospects.
"Everybody talks about his athleticism," Twins scouting director Deron Johnson said. "He's got a really good swing. We think he's going to hit. We think he'll hit anywhere from No. 1 in the order to No. 3. Tremendous, tremendous upside."
University of Florida catcher Mike Zunino, who has drawn comparisons to Jason Varitek for his leadership and ability to handle a pitching staff, was taken No. 3 overall by Seattle.
"For me, my most important thing is I take pride in my defense," Zunino said. "Whether it's calling games, or receiving or blocking, that is what really defines me as a player."
Baltimore went with LSU right-hander Kevin Gausman with the fourth pick, adding a potential ace to its system.
Kansas City took University of San Francisco right-hander Kyle Zimmer, a converted third baseman, with the No. 5 overall pick.
"He was the No. 1 pitcher on our board," said Lonnie Goldberg, the Royals' director of scouting. "I think everyone should know that. He's the guy we wanted."
The draft opened with uncertainty about the talent — many teams considered this crop of players weaker than recent groups — and several significant rule changes in place.
Under baseball's new collective bargaining agreement, teams will have a pool of bonus money from which to sign players. They'll also face a punitive tax and the possibility of losing draft picks if they go over the prescribed bonus total. If a player doesn't sign, the team loses the amount for that slot. Clubs now have until mid-July to sign draft picks, instead of the previous mid-August deadline.
"Let's see how it works out," Selig said. "I am very optimistic. I think this will work out very well. And I think these are changes clearly helping the game."
The first round and the initial compensation round were completed Monday night, with rounds 2 through 40 conducted through Wednesday via conference call.
AP Sports Writers Tim Booth in Seattle, Dave Campbell in Minneapolis, Mike Fitzpatrick in Secaucus, Kristie Rieken in Houston and David Skretta in Kansas City, Mo., contributed to this report.