New York — Mike Shula changed into shorts and a team-issued T-shirt for a workout recently at the Giants’ facility in East Rutherford, N.J., and as he walked into the gym he passed a mirror and did a double-take at the logo on his chest.

It’s really happening, he thought. I’m really coaching for the New York Giants.

Shula is football royalty, the son of the great Hall of Famer Don Shula, the winningest coach in NFL history.

But Mike Shula, 52, the Giants’ new offensive coordinator and quarterbacks coach, comes off as a grounded everyman. He walks with a quiet confidence and speaks assuredly and relatably, a lot like the head coach who hired him, Pat Shurmur.

He and Shurmur, also 52, who is from Dearborn Heights and played and coached at Michigan State, seem to share not only certain qualities as coaches but opinions on what’s important in a QB. And that’s pertinent because Shula essentially has been running point on the Giants’ search for a potential franchise quarterback in this month’s NFL draft.

“What’s their personality? What’s their demeanor like?” Shula said of what he’ll try to learn from quarterbacks Josh Allen (Wyoming), Josh Rosen (UCLA), Sam Darnold (USC) and Baker Mayfield (Oklahoma) in private visits to the Giants’ facility next week. “You can talk a little football. We’ve seen them work out now. Just re-establish that relationship. When you’re looking and getting ready to invest a lot in somebody, you want to find out as much as you can in every aspect of their life.”

Now granted, Shula for the past 7 years has coached a pretty good quarterback with a strong personality — maybe you’ve heard of him: Cam Newton of the Carolina Panthers. Talent trumps all. So if the Giants feel one of these QBs is clearly above the rest and he’s available when they pick second overall, they are expected to take him.

No position sets the tone of a team more than its quarterback. And so, if GM Dave Gettleman and Shurmur and Shula are consistent with this philosophy when they evaluate QBs, this is probably a differentiating factor that sheds some light on what direction they might lean.

Start with this: Davis Webb, the rising second-year QB already in the building, feels like the kind of committed worker, born leader and quiet killer Shurmur and Shula would love.

The lack of NFL game tape on Webb may force the Giants to draft a quarterback at No. 2 anyway, for fear of the unknown. Shula even admitted he hasn’t quite gotten a handle on Webb yet since the coach has been on the road so frequently. He reiterated the Giants’ pre-draft minicamp from April 24-26 is an important three days for Webb.

If the Giants do draft a QB, though, the humble-but-impressive Allen and the easygoing-yet-driven Darnold feel like they could fit the profile of what Shurmur and Shula value most.

Allen, in particular, feels like an intriguing personality fit to go with his impressive physical skills. Shurmur said at the league meetings that Allen is “tough” and “competitive,” which are “traits that I admire in a quarterback.” Shurmur admitted he’s had more exposure to Allen than any of these QBs.

And Allen at the NFL combine in early March clearly felt Shurmur was a great fit for him: “I’d want to play for him because he just had this kind of silent vibe to him,” Allen told the Daily News. “He was kind of reserved, and at the same time I can feel his presence and understand how much he loves football, how much he knows football.”

That said, this doesn’t mean the more vibrant personalities of Rosen and Mayfield will be turnoffs, either.

Rosen looks like the best pure passer in the draft and could be a voice and leader born for the New York market, while Mayfield won the Heisman Trophy for a reason.

Plus, it’s gone somewhat under the radar, but Shula has done a ton of work on Mayfield, including a private workout together at Oklahoma’s mid-March pro day. And if Shurmur and Shula value the qualities of tough and competitive, Mayfield passes that test easily.

Cards claim ex-Lion

The Arizona Cardinals have been awarded waiver claims on quarterbacks Brad Doughty from the Miami Dolphins and Alek Torgersen from the Lions. Neither has thrown a pass in the NFL.

Torgersen was an undrafted rookie free agent out of Penn last year and spent the season on the Washington and Detroit practice squads. Doughty was a seventh-round pick of the Dolphins in 2016 and spent the last two seasons on the practice squad.

Extra points

Running back Stevan Ridley and wide receiver Justin Hunter signed one-year deals to stay with the Pittsburgh Steelers.

... Punter Marquette King signed a three-year, $7 million contract with the Denver Broncos less than a week after his surprising release from the Oakland Raiders.

... The Giants have signed durable cornerback William Gay.

Associated Press contributed.