He was well known, particularly for his movies with Erroyl Flynn like Santa Fe Trail, but was not a top tier movie star. Critics (and Reagan himself) regarded Kings Row (1942) as his best work. At release many thought the movie would contend for Oscars and it went on to receive a nomination for Best Picture, though it did not win. Reagan would use his famous line from the movie "Where's the Rest of Me?," as the title of his 1965 autobiography.
It was generally expected that his appearance in the movie would signify his big break and emergence as a major star, but WWII interrupted his career. He served in the 1st Motion Picture Unit during the war and helped make training videos for new recruits. This took him away from the studio and prevented him from being in any major releases. After the war, the studio regarded him as too old to give a significant role to and his career as a movie star began to fade. His first wife, Jane Wyman, would win an Oscar for Best Actress in 1948 as he languished unused at their ranch.
Despite his failure to become a top tier movie star, Reagan's peers held him in high regard. They elected him to lead the Screen Actors Guild (SAG) seven times, making Reagan the only President to serve as head of a labor union. In this capacity he dealt with McCarthyism and the movement away from the exploitative system where studios essentially had exclusive use of actors.
Reagan was well known as an actor when he ran for Governor of California in 1966, and his opponent, George Christopher, tried to use it as proof of his inexperience/unworthiness for office. The attacks largely failed and despite attempts to portray Reagan as intellectually inferior, he won by a comfortable margin.
There's room for more input here (it would be difficult to measure 'how popular'), but you can get started on these earlier responses