Sullivan said he didn't dunk in a game until the home finale against LSU, and has dropped about 15 pounds in the offseason.
"The explosive Frankie is back," Barbee said. "He's been making shots, he's been making plays and that's what we need from him this year."
Guard Chris Denson is back after averaging 8.7 points in 22 minutes a game.
The Tigers are still seeking a point guard to replace Varez Ward, who left the team while under investigation for alleged point shaving.
The freshmen Price and Greene join 5-foot-10 senior Josh Wallace, who was placed on scholarship before this season. Wallace is quick and a strong defender but Barbee said Greene is explosive and athletic and Price is "offensively as talented as anybody we've got on the team."
"I think we've got a three-headed monster," Barbee said. "It's probably the deepest we've been at the point in terms of quality production and play, and all three of them bring something different to the table."
The Tigers still need to develop some scorers alongside Sullivan
They were 10th in the SEC with a 62.6-point average last season and 11th in 3-point percentage (30.2).
Making the postseason still seems like a longshot for a team that hasn't been to an NCAA tournament since 2003 or the NIT since 2009. Chubb is optimistic about the Tigers' potential.
"We definitely have a postseason-caliber team," said Chubb, who averaged 8.1 points and 5.1 rebounds. "The players are a lot bigger, better, faster, stronger than we've ever had. Some of these freshmen coming in physically have the bodies of some of the seniors that were leaving last year."
The Tigers open the season Nov. 15 against Murray State.