Richard Marx is out to make his mark tomorrow night at the Bayou. His recently released debut album, "Should Have Known Better" on the Manhattan Records label, is climbing the pop charts, and his single "Don't Mean Nothin'," featuring Joe Walsh on guitar and vocal harmonies by Randy Meisner and Timothy B. Schmidt of the Eagles, is ranked a healthy 33.

"I think the first sound that came out of my mouth was in tune," said Marx. And for most of his 23 years he has been devoted to music. At age 5, he was singing jingles for such products as Peter Pan peanut butter and Ken-L-Ration.

But it took Lionel Richie to give Marx his first "real" break. "I worked with him on three of his albums doing background vocals," says Marx. "I owe him a lot." Meanwhile, Marx cowrote two Kenny Rogers hits, "What About Me" and "Crazy," as well as Chicago's "Good for Nothing" and Philip Bailey's "Love Is Alive."

Marx's six-member band includes drummer Mike Derosier, former member of Heart, and guitarist Paul Warren, who played with Tina Turner. Their performance begins at 9 p.m. Tickets at the Bayou,at Wisconsin and K streets in Georgetown, are $8.50. For more information, call 333-2898. FEASLEY'S SINGING GUITAR

When classical guitarist William Feasley was a kid, he wanted to be a Beatle. Problem was, he says, "I couldn't sing."

Practice couldn't give him a voice, but it could make him into a fine guitarist -- which he'll demonstrate at a concert at 6 p.m. tonight at Bradley Hills Presbyterian Church, 6600 Bradley Blvd. in Bethesda.

Feasley's recital will show the range of the guitar repertoire, from the rococo to the contemporary. Organist Donald Sutherland will join him in a program that will include Giuliani's "Primo Concerto," Op. 30 in A, Boccherini's "Introduction and Fandango" and Bading's "Variations on an Old Dutch Love Song."

Tonight's performance will benefit the Manna Food Center, a local organization that distributes food to the hungry; a $5 donation is requested. For information, call 565-0458. THE RICH LIFE OF JAZZ Washington-based jazz vocalist Lisa Rich can barely remember life before jazz. "I have been a jazz professional since I was 13 years old -- all right, I was only paid $5, but I was making money."

When she was 20, Rich produced her own album, "Listen Hear." Since then she has been performing throughout the world.

Rich enjoys touring but these days she is at least as involved in teaching. "I recently taught an eight-week course through the Smithsonian Resident Associates Program," she says. "We had all kinds of people, from professionals to people who had never sung a note. I try to provide the kind of training in jazz performance that wasn't available when I was learning. Sure, there's a certain amount that still has to be learned 'on the bandstand,' but there is an awful lot that people can tell you before you get up there."

Rich will be on the bandstand Friday and Saturday at the Park Place Cafe. She'll do two shows each evening, the first beginning at 9 p.m. For information, call 667-2701. THE BEST OF BUCKLEY

The Wolf Trap Opera Company is known for promoting and developing the talent of young opera performers. This summer, the company will benefit from the experience of conductor Richard Buckley, a seasoned professional at age 33.

Buckley, who earned his masters from Catholic University at age 20, spent nine years with the Seattle Symphony, eventually becoming its principal guest conductor. At 30, he became music director of the Oakland Symphony and has conducted the New York City Opera and the BBC Symphony. He was a prize winner at the 1979 Besancon Competition and the 1982 Rupert Foundation International Conducting Competition.

"Art is an expression of inner dialogues of thoughts and feelings," say Buckley. And, "music is the distillation of emotion ... I attempt to find in my interpretation that parallel emotion of the composer when he or she wrote the original ... "

Buckley will conduct the Wolf Trap Opera's production of Rossini's "The Barber of Seville" today at 2 and Wednesday and Friday at 8 p.m. at The Barns of Wolf Trap. Call 938-2404 for ticket information.