While sitting in the media room Thursday at the Al McGuire Center and listening to Bill Cords discuss Marquette’s coaching vacancy, two traits became apparently clear for a coach to be considered for the job.

First, a track record of success at a major program.

“We feel we have everything in place in terms of support and facilities to make sure that person has a chance to do what we all want to do and that’s get back to the Final Four and win a national championship,” Cords said Thursday. “That’s our vision.”

Now, every school aspires for that.

But Marquette legitimately has the resources to compete for a national championship — that’s what happens when you only get outspent by Duke on your basketball program — and that’s why the second thing is commitment.

Second, Cords and company want the man who replaces Buzz Williams to consider Marquette a career-changing opportunity.

“Well, we’re not a steppingstone,” Cords said of the Marquette job. “There’s one time where you might say that, but I don’t think we are now.”

And Marquette is acting like a non-steppingstone with regards to the candidates it’s considering — despite getting dumped by its second coach in six years.

Just look at who Cords and company have pursued or are pursuing.

Shaka Smart.

He has transformed Virginia Commonwealth into a consistent top-25 team and NCAA Tournament contender. He spurned UCLA last offseason and now has done likewise to Marquette.

There’s no shame in failing to catch the Loch Ness Monster.

Ben Howland.

(No, I don’t know why he’s listed as a redshirt in his UCLA bio.)

He took UCLA to three consecutive Final Fours (2006-2008) and posted an 89-40 mark in four seasons at Pittsburgh when it was in the Big East. And he reportedly wants the job, badly.

Cuonzo Martin.

This name doesn’t have the sex appeal of a Ben Howland, let alone a Shaka Smart, but the Tennessee coach is coming off of a Sweet 16 appearance at a football-based institution. And, despite reportedly not having the full support of the university, this Paint Touches report explains why he’s a noteworthy candidate.

Mike Hopkins.

The man has been by the side of legendary coach Jim Boeheim since 1995 and is likely the heir apparent to the college basketball icon. He lacks experience as the man in charge, but he’s been around and soaked in plenty of success.

Brian Wardle.

The former Marquette standout and assistant coach has UW-Green Bay on the rise after the Phoenix won the regular-season title in the Horizon League. He’s shown a good eye for recruiting, landing athletic 7-foot-1 center Alec Brown and scoring machine Keifer Sykes. Give him the Marquette resources and the Golden Eagles could have a home-grown hit.

Steve Wojciechowski.

Once you get over the shock of the name and read this Paint Touches report, you’ll wonder why no one else has picked up on Wojciechowski before. With 15 years under Duke legend Mike Krzyzewski, Wojciechowski, like Hopkins, has been around success and played a key role in it.

“The program is the strongest it’s ever been. Solid base, foundation, support, everything,” Cords said of Marquette. “Therefore, our pool is good. It is stronger and better than by far than we’ve had. We’re going to have an opportunity to find the best possible coach we can find.”

Commitment. Previous success as a head coach of a major Division I team.

Those appear to be the two most important pieces Marquette’s considering.

And based on those criteria alone, Howland should be Marquette’s man.

He doesn’t come without baggage, as this Sports Illustrated column explains, but he’s had success on the biggest of stages as a recruiter and tactician. And, at 56 years old, he isn’t likely interested in playing college basketball coaches’ version of musical chairs.

Martin is the only other candidate on this list with experience of success as a major Division I coach — sorry UW-Green Bay — and although Hopkins and Wojciechowski have been key cogs in winning programs they haven’t been the one steering the wheel.

That’s not me knocking them for that.

But based upon Cords’ comments Thursday and a source that told Paint Touches that Marquette wants an experienced head coach who has had “elite success,” that would seem to cross them (and Wardle) off of the list.

(Cords said he would consider a coach with any kind of background at Thursday’s news conference, but Marquette appears to desire a seasoned head coach.)

Given that Martin’s success is more recent and limited — and that at 42 years old and no ties to Marquette who’s to say this isn’t a steppingstone job for him? — Howland should trump Martin.

That’s making this process far simpler than it is in reality, but sometimes there’s no need to complicate things.