An internal House investigation of alleged South Korean influence-buying in Congress took a step forward yesterday when the Democratic steering committee approved Speaker Thomas P. (Tip) O'Neill Jr.'s personal choices to fill three vacancies on the House ethics committee.

Reps. Lee Hamilton of Indiana, Richardson Preyer of North Carolina and Walter Flowers of Alabama were picked to replace retiring Rep. F. Edward Hebert of Louisiana, and Reps. Thomas Foley of Washington and Melvin Price of Illinois, who both stepped down because of their duties as chairmen of other committees.

Rep: Millicent Fenwick of New Jersey had been picked earlier to fill the lone Republican vacancy on the 12-member panel.

Rep. John J. Flynt (DGa-.), chairman of the committee which has often been criticized for failing to actively purse allegations of misconduct by members, said yesterday that he was "thrilled" with O'Neill's selections.

"I gave the speaker a sort of wish list last week of my recommendations for new members and all three of them were on it," he said. "I'm anxious now to get the committee organized so we can begin our work."

A public clamor for the ethics committee investigation followed newspaper reports last fall that South Korean President Park Chung Hee personally directed an elaborate lobbying effort in which members of Congress were given gifts and cash totaling hundreds of thousands of dollars a year.

At least 20 present and former members of the House are known to be under Justice Department scrutiny because of their ties to the Korean lobby.

O'Neill's choices for the committee vacancies were viewed as an early test of his willingness to back up his oftrepeated promise to press for a stricter code of ethics for House members.

Early responses to his selections were overwhelmingly favorable. Fred Wertheimer, vice president of Common Cause, the government reform lobby, said, "Tip O'Neill deserves a lot of credit; They're very impressive choices."

Rep. Floyd Spence (RS.C.), the ranking minority member, said yesterday, "I'm pleased with all of them. They have good reputations from all quarters."

All three new members said O'Neill asked them personally on Wednesday to serve on the committee.

Hamilton is a member of the House International Relations committee, which also is considering an investigation of the South Korean affair. He also is a member of a special commission now working on recommendations for tightening the ethical standards of the House.

The other two Democratic newcomers also have had recent experience with House rules of conduct. Preyer, a former federal judge, said yesterday, "I guess we're on some sort of binge on ethics."

O'Neill already had tapped Preyer to head a special ethics committee to write a new code of public conduct for the House.

Flowers, who as a southern conservative, was considered a pivotal figure when he voted for the impeachment of Richard Nixon in the House Judiciary Committee in 1974, is chairman of a subcommittee that considered stronger financial disclosure and lobbying bills in the last session.

New committee members and chairmen must be approved by the Democratic caucus and the full House next week before the ethics committee can formally organize for the investigation.