The actor and director who was born in Wales and now resides in London said he knew he wanted to be an actor when he was 9-years-old.
"The family assumed it was just a thought, and it would be a phase," Baxter said.
At age 13 Baxter got a walk-on role in a production, which confirmed his love for acting.
"I just knew. I felt very sure of myself, and I knew that was going to be my life," he said.
"Various people were wheeled in to talk to me about how uncertain the life of an actor was, but no one ever succeeds without someone pushing them in the background and a teacher talked to my parents about letting me try."
After serving in the army for about two years, Baxter returned to England to attend drama school.
"The army was a wonderful experience because I was living with people I would have never met in my normal life," Baxter said. "Before the Army I was still sending my laundry back home."
Wanting to get a break in acting and working as a dishwasher to pay the bills, Baxter said he took a chance when he was 25 to audition for Orson Welles.
"I was bored and depressed. I wanted to be a star and be a star quickly in the theater. I didn't quite know what to do," he said. "I felt I had nothing to lose."
His perseverance paid off when Welles brought Baxter on a theater tour.
The tour ended early, and Baxter said he was concerned about going back home and again struggling to be an actor.
He said Welles had faith in Baxter's talent and told him so.
"It was the magic words of Orson Welles that changed my life," Baxter said.
His first appearance in New York as the young Henry VIII in "A Man For All Seasons" in 1961.
"My career just took off," Baxter said.
"If you're going to be a huge success the best place to be so is New York. Troops of people come into the dressing room to talk to you. You meet all kinds of wonderful people who truly appreciate what you do."
The part won him Theatre World's 'Most Exciting New Broadway Actor' Award.
"It was just wonderful, and it altered my whole life from so trying to get work to being work-sought," Baxter said.
He was the original star of "Sleuth" in London and on Broadway, and was Prince Hal with Orson Welles and John Gielgud, Valentine in "You Never Can Tell," and Bob Acres in "The Rivals" with Ralph Richardson.
He has played Benedick, Hamlet, Macbeth and Antony, and was Elyot in "Private Lives" with Joan Collins.
He returned to New York in 2001 in "The Woman In Black." Baxter worked with actresses such as Elizabeth Taylor and dames Judi Dench and Maggie Smith.
Having done some directing work at the Shakespeare Theatre in Washington D.C., Baxter met PJ Paparelli who now serves as artistic director of Juneau's Perseverance Theatre.
Baxter said Paparelli called him during the summer and woke him at 3 a.m. to ask him to direct "Noises Off," a British farce, at Perseverance Theatre.
"He had gotten the time wrong and the phone rang in the middle of the night. I said 'you've got to be absolutely mad,' and I put the phone down," Baxter said.
"I was telling a friend about it and he told me that I had been mean and that I respected PJ and that I should go see Alaska. I telephoned PJ right back to tell him I was coming."
Baxter is currently directing company members for the show, which opens Saturday, Nov. 11.
"I just love it here. The cast is wonderful, and Alaska is so beautiful," Baxter said.
"Judi Dench called me yesterday and asked me if I was living in an igloo. I told her that Juneau is very sophisticated."
Paparelli will conduct an actor's studio interview with Baxter about his career as an actor and backstage stories at 6:30 p.m. Monday, Nov. 13, at the theater. Tickets are $5 at the door