INDIANAPOLIS — With the first draft pick of their just-launched, winning-with-class era, the 49ers select ... Dorial Green-Beckham?

Green-Beckham is considered the most talented member of this year’s strong class at wide receiver, a position that likely tops the 49ers’ list of draft needs. However, the 6-foot-5, 237-pound pass-catcher comes with a catch: Green-Beckham is this year’s poster boy for the dogged-by-character-concerns draft prospect.

“Dorial Green-Beckham is as gifted as anybody in this class,” NFL Network draft analyst Mike Mayock said, “but you better do your homework off the field.”

The 49ers have the No. 15 pick and a recent pledge from CEO Jed York that they’ll be “winning with class” after six of their players combined for 10 arrests since 2012. In December, York acknowledged he let standards slip while the 49ers reached three straight NFC title games from 2011-13.

“We did things,” York said, “that probably doesn’t gel well with who I am.”

This leads back to Green-Beckham, who entered Missouri as the nation’s top-rated high school wide receiver in 2012 but was dismissed from the team in April after his third off-the-field incident.

After two marijuana-related arrests, he was accused of forcibly entering an apartment and pushing a woman down at least four stairs. He wasn’t arrested, primarily because witnesses feared retaliation if they filed a criminal complaint, the Associated Press reported. Green-Beckham transferred to Oklahoma but didn’t play for the Sooners last year and declared for the draft after playing two college seasons.

On Thursday at the combine, Green-Beckham fielded a flurry of questions regarding his off-the-field missteps. He made five references to his desire to prove he is a “better person.”

“All the decisions I’ve made, I wish I could take (them) back,” he said. “It happened. I was young. I made mistakes. I understand that. I just want to focus on one thing, and just look forward to this draft and being the best I can be.”

Green-Beckham’s best on the field explains why a team could roll the dice and use a high-end pick on him. In 2011, at Hillcrest (Mo.) High, he was the first wide receiver in 22 years to be named USA Today’s Offensive Player of the Year, and recruiting analyst Tom Lemming termed him the best wideout prospect since Randy Moss. In 2013, he had 59 catches, 883 yards and led the SEC with 12 touchdown catches.

Mayock ranks Green-Beckham fourth among wideouts in this year’s draft class behind West Virginia’s Kevin White, Alabama’s Amari Cooper and Louisville’s DeVante Parker. The top three could be off the board when the 49ers select at No. 15, meaning they could have a chance to grab Green-Beckham, whom Mayock views as a mid-first-round pick.

Before the draft, 49ers quarterback Colin Kaepernick could offer the front office his assessment of Green-Beckham. The pair have both been working out at EXOS traning facility in Phoenix during the offseason. On Wednesday, 49ers general manager Trent Baalke wasn’t asked specifically about Green-Beckham, but he did address how the team investigates the backgrounds of draft prospects.

“We try to be as thorough as possible, do as many background checks as we can and talk to as many people as we can,” Baalke said. “Get on the Internet and dig as much as we can with all of the social media stuff and everything. … But there are a lot of unknowns, and that’s not going to change. And there is a risk-reward to this business, and that’s not going to change.”

That risk-reward dynamic has been illustrated by several high-profile college wideouts who have arrived in the NFL with off-the-field concerns in recent years. Dallas’ Dez Bryant, a first-round pick in 2010, has become a two-time Pro Bowler. However, two other high-end picks, Cleveland’s Josh Gordon (second round of 2012 supplemental draft) and Jacksonville’s Justin Blackmon (No. 5 in 2012) have served multiple substance-abuse-related suspensions.

“What happens sometimes is the ability and talent of the athlete overwhelms the other analysis, and that’s where we make a lot of mistakes,” Mayock said. “Green-Beckham this year is going to be a polarizing conversation.”

More than two months before the draft, the 49ers are likely having conversations about the prospect with tantalizing ability and a troubling past.

“I know what’s at stake,” Green-Beckham said. “I know what type of person I am. I understand what the NFL is looking for (from) me as a person. I just want them to know I’m going to go out there and give it my all.”

Eric Branch is a San Francisco Chronicle staff writer. E-mail: ebranch@sfchronicle.com. Twitter: @Eric_Branch