WALTHAM — The Celtics’ four new draft picks stepped onto a makeshift stage that had been constructed above the team’s practice court Tuesday. They held up their new green jerseys with their new white numbers and they forced smiles amid the snap-snap-snapping of cameras.

The mood was light. President of basketball operations Danny Ainge made a joke about guard Terry Rozier’s fancy glasses, wondering if they were prescription or strictly cosmetic.

Rozier chuckled about how he hadn’t received much advice about Boston from his former coach at Louisville, Rick Pitino, who had a mostly forgettable tenure as coach of the Celtics. Current Celtics coach Brad Stevens smiled and — once more — told the story of how he had tried to recruit 28th pick R.J. Hunter away from his father.

About 20 feet from the stage, Hunter’s parents, Ron and Amy, sat in folding chairs and beamed as they watched R.J. realize his dream along with the three other prospects: Rozier, LSU forward Jordan Mickey and William & Mary guard Marcus Thornton.

But it did not take long for the jovial mood to slowly shift, for Ainge and Stevens to provide gentle reminders that the difficult part begins now.

“From a basketball standpoint,” Stevens said, “I think the next four days, starting [Tuesday], are as important as any days they’ll have.”

He was referring to the sets of two-a-day practice sessions that will precede the team’s lengthy journey out West, where it will play in consecutive summer leagues in Salt Lake City and Las Vegas.

Ainge added: “It’s each one of these guys’ jobs to prove that Brad needs them. And their play this summer, it begins there. And their work leading up to the season and training camp, everything they do will be noted, their work ethic and their character and their performance.”

Yes, the cushy welcomes were over. It was time to get to work.

Although the Celtics failed in their numerous attempts to move up in last Thursday’s draft, they say they are pleased with the four-player class they assembled. Team executives have spoken especially glowingly about Rozier, whose selection at No. 16 overall came as a bit of a surprise to experts and fans.

On Tuesday, Ainge said that he had considered trading down to take Rozier lower in the draft. But they believed other teams were in hot pursuit and ultimately determined that trading down would be too risky. Ainge and Stevens have raved about Rozier’s athleticism, defense, speed, and toughness. Rozier, for one, is eager to prove that he was worthy of the early praise.

“I’m not so worried about how many guards we’ve got,” he said. “I’m just worried about how I can come in and fit for this team, fit for this league, and help my team improve.”

If the selection of Rozier came as a surprise to others, the selection of Hunter at No. 28 came as a surprise to, well, Hunter. The sharp-shooting guard said he had to cancel his scheduled predraft workout with the Celtics because he was ill and he was unable to find a new time to come to Boston.

He thought he had hurt his chances here, but then he got the call on draft night that made it clear he had not.

“I guess I was the mystery man,” Hunter said, “so it ended up working out.”

The 6-foot-8-inch Mickey, who led the nation in shot-blocking at LSU last season, should bring much-needed athleticism to the Celtics’ frontcourt.

“He was the best athlete there,” Ainge said. “Very long and athletic. He can switch [defensively] and it’s a big thing having big guys that can protect the rim and switch and guard perimeter guys, and we think that Jordan can be one of those guys.”

Ainge also reiterated that Thornton, who was selected with the 45th pick, would most likely be stashed on a D-League roster or on a European professional team next season. Thornton said the Celtics made him aware of that possibility during the predraft interview process, but insisted that he will first fight for a roster spot.

As the new crop of rookies prepared to join the rest of the summer league roster at Wednesday’s practice, Ainge was preparing for a busy time of his own, with free agency beginning at 12:01 a.m. It continues to appear that the process will fail to yield the bounty that some Celtics fans had been hoping for.

Boston is not expected to be in the mix for the elite free agents, and the team will be cautious about moves that limit future flexibility.

“You want to get the best players,” Ainge said, “but you also have to manage the salary cap and the payroll to keep us competitive. So those will be two priorities.”

The Celtics have submitted a qualifying offer to forward Jae Crowder, making him a restricted free agent. That means that Boston will have an opportunity to match any offers Crowder gets from other teams.

Tony Dutt, forward Brandon Bass’s agent, said numerous teams are expected to have interest in the 10-year veteran as free agency begins. Dutt added that Bass would be open to a return to the Celtics.

“I think Brad and Danny understand the value of what Brandon brings,” Dutt said by phone. “He loves Boston, and if it works out for him to stay there, we’d be more than happy.”

Adam Himmelsbach can be reached at [email protected]. Follow him on Twitter @adamhimmelsbach.