All three are from Georgia, which is why the news conference was held on a humid Saturday afternoon at Turner Field before the Rangers faced the Braves.
"I'm really excited," said Matthews, a left-hander who was the 33rd overall pick. "It has always been my dream to play professional baseball. I can't wait to get started."
Cone and Matthews won't have to wait long. Cone is being assigned to Class A Spokane in the short-season Northwest League. Matthews will play for the Arizona Rookie League Rangers.
"We wanted to get these guys out playing," Fagg said. "As an organization, we wanted to make sure we drafted guys who are high character, high makeup guys who have talent. We feel we have that in these guys."
Taylor will remain behind in Georgia. He remains partially paralyzed with a broken neck after a March 6 collision with Cone. They were playing the outfield for Georgia against Florida State. They both went for the same ball in left-center. They both dove for it and collided. Taylor's head hit Cone's hip, fracturing two vertebrae in his neck.
His season was over. He has not walked since, but Texas still took him in the 33rd round. It may have been a nice but futile gesture. Taylor does not believe that.
He would have been a 7-to-12th-round pick if not for the injury. Ryan Coe, the Rangers' relentless area scout in Georgia, was watching Taylor closely as well as Cone. Taylor still believes he will play again.
"Right now, my goal is just to get better ... get my legs under me," Taylor said. "Keep getting my work in and get back on the field. "
The Rangers met with Taylor, but will not sign him to a contract right away. They have made a substantial donation to help with his recovery, but the plan is for Taylor to remain at the University of Georgia. He will do his rehabilitation work there, finish his schoolwork and get his degree.
"That's most important," Taylor said.
"You talk about a special person ..." said A.J. Preller, the club's senior director of player personnel. "His goal is to get better every day, that's what we put in front of all our players. That's what we're putting in front of Zach and Kevin ... do something to get better each and every day."
If Cone and Matthews do that, they could be in the Major Leagues someday. With Taylor, that is not quite as clear, but the hope burns bright and he was all smiles on Saturday afternoon as he met with the media and then with the players.
"I'm a big fan of the Texas Rangers," he said. "I never thought this would happen. It's a great opportunity just to be here."
Cone had a big smile on his face, but this has been difficult for him, too. He had a rough junior season at Georgia. His offensive numbers were way below what they were in his sophomore year. His batting average alone went from .363 to .275. But the Bulldogs made a surprisingly late run in the season and were able to win a berth in the NCAA Tournament. That lifted everybody's spirits and Taylor was in the dugout for the tournament games.
"There were a lot of ups and downs to go through what we went through," Cone said. "It wasn't easy. But to see J.T. getting better, to see our team make a run, to get drafted by the Rangers and to see J.T. up here, it's pretty sweet.
"This shows a lot about the Rangers and their organization and how they are about their players. To be here with and be teammates with J.T., it's awesome."
Both Cone and Matthews signed quickly. They are two of just nine players from the top 60 picks that have signed to this point. Matthews, who had a scholarship waiting at the University of Virginia, is one of just three players taken in the first round who have signed.
"It was a very difficult decision," Matthews said. "Virginia is a really good school both baseball and academically. But I've got an opportunity to play professionally."
Cone also signed quickly even though he is advised by Scott Boras, who has been known to take all summer and go right down to the deadline before his players sign. But Cone wanted to be with the Rangers on Saturday, and to have Taylor sitting next to him made it even more special.
"This really is awesome," Cone said.