WASHINGTON - Many people hailed President Reagan's choice today of Arizona Judge Sandra O'Connor to fill the vacancy on the Supreme Court, but anti-abortion leaders and the head of the Moral Majority vowed to fight the nomination. At a news conference in Phoenix O'Connor said Reagan telephoned her yesterday afternoon and told her she was his choice. But she repeatedly refused to discuss abortion, equal rights for women or any other "substantive questions pending the confirmation hearings." A beaming O'Connor kissed her husband and three sons and told reporters who questioned her lack of federal judicial experience: "Time will tell whether I have a lot to learn." Asked to describe her feelings on being the first women appointed she said: "I don't know that I can. In approaching the work on the bench I will approach it with care and effort and do the best job I can do." Former President Nixon called the nomination of O'Connor, who served as co-chairman of Arizona's state committee to re-elect Nixon "a dramatic breakthrough for women, the court and the nation." But the Rev. Jerry Falwell of Moral Majority condemned the selection, saying: "Either the president. did not have sufficient information about. Judge O'Connor's background on social issues or he chose to ignore that information." Her "record indicates she is not an opponent of abortion on demand and is opposed to attempts to curb this biological holocaust ... ," he said. The National Right to Life Committee, which voiced