Wanted: One quarterback. Experience not required but preferred. Must be able to throw a ball accurately to players in like-colored uniforms and run respectably. Contact D. Bestwick, Charlottesville, Va.

Virginia football coach Dick Bestwick hasn't gone so far as to take out a classified ad yet, but before the season is over he may wish he had.

"If I was one to get headaches I guess I would have one," Bestwick confessed. "I guess I'm lucky I don't get them."

Bestwick second-year coach at Virginia, has a number of problems that would give anyone a throbbing between the temples.

This is not surprising when a team is coming off a 2-9 season, even if the 2-9 record represented a remarkable improvement over the year before.

"We're going to be a very young team for another year yet," Bestwick said. "We still don't have that nuclens of 12 to 18 solid seniors that you need. But we've got more experience this year than last and next year we'll have more."

With nine starters back on defense, including captain Sam Pfabe, who will play nose guard - his third position at Virginia - the Cavaliers should give up fewer than the 416 yards per game they yielded in 1976.

The offense is another story. The most reasonable facsimile of a quarterback Bestwick had a year ago, Andy Hitt, has graduated. Drew Schuett, who transferred from Notre Dame to get more playing time at quarterback, is now a defensive back.

Now the quarterbacks are named Phil Spencer, Chip Mark, Wally Marcus, Robert Anderson, Ted Manly, Quentin Murray, Bryan Shumock and George Spady. Others may be added later. Total experience: none.

"We're going to start everyone even and see what develops," Bestwick said, "I honestly don't know who the best one is. I hope we'll be able to come up with someone who will run our offense effectively."

A difficult task. Whoever does end up at quarterback will have rookie running backs to work with. Starters David Sloan and Billy Copeland have graduated, as have flanker Joe Sroba and split end Tommy Fadden.

Paul Izlar, a transfer from Vanderbilt who looked good in spring practice, and Tommy Vigorito, Bestwick's top recruit, likely will be the starting running backs. Nevertheless, the offense, which averaged just eight tenths of a fumble per contest last year (one of the team's few positive statistics) is going to be extremely young.

If they make mistakes early they will pay for them. Two of the first three games are against conference opponents. North Carolina State in the opener and Duke two weeks later. For a breather in between, the Cavaliers play Texas in Austin.

Neverthless, Bestwick, who took over midst the chaos created by Sonny Randle's tumultuous 1-10 final season, remains optimistic.

"What we have to do this year is not make mistakes that put our backs against the wall," he said. "We're not good enough yet that we can afford to beat ourselves.

"As we get better and get more good athletes we'll be able to recover from mistakes: it will be harder for teams to beat us unless we beat ourselves. Now we have to be sure not to beat ourselves because there are many ways we can be beaten."

Virginia will give up fewer points this year. Whether or not the 2-9 mark is improved (both wins were by one point) depends on the offense. And the offense depends on whether or not Bestwick finds a quarterback.