C. William Verity Jr. traveled to Capitol Hill yesterday to call on his senator, Ernest F. Hollings (D-S.C.) -- who also is chairman of the Senate Commerce Committee, which will consider the nomination of the retired steel executive to be secretary of Commerce.

Verity, 70, whom President Reagan nominated to replace the late Malcolm Baldrige, recently switched his voting residence from Middletown, Ohio, to South Carolina, where he maintains a home in the coastal resort town of Beaufort.

Hollings promised quick consideration of Verity's nomination, probably soon after Congress returns from its summer recess on Sept. 8.

"I do not see any reason why we should hold up Mr. Verity's nomination," Hollings said. "I know we will not agree on every issue, but he is the president's choice. He is competent and has good solid business credentials. I believe we can work together to make America more competitive."

Verity, who retired in 1982 as chairman of Armco Inc., the steel company that his grandfather founded in 1900, is a familiar figure in Washington business and political circles. He gained the admiration of Reagan early in the administration's first term when he served as chairman of the White House private sector initiative.

"The chemistry that Verity had with the president in the private sector initiative panel was very good," said Alexander (Sandy) Trowbridge, president of the National Association of Manufacturers, a Commerce secretary in the Johnson administration and a member of that commission. "The two liked each other from day one."

Verity also used to talk about foreign policy goals with Cyrus Vance, secretary of State under President Carter, and considered himself a friend of Soviet leader Leonid Brezhnev as a result of his advocacy of greater trade ties between the United States and the Soviet Union.

As cochairman of the U.S.-U.S.S.R. Trade and Economic Council, Verity has been an outspoken critic of the use of export controls to reach foreign policy goals. He said the tactic, used by Carter and Reagan against the Soviet Union, hurt American businesses without accomplishing U.S. aims.

Verity, though, supports strict limits on the sale of sensitive technology to the Soviet bloc. He agreed with Baldrige that this can't succeed with only U.S. participation but depends on strong cooperation by U.S. allies, associates said.

Verity's stance on Soviet trade is likely to provide the major fireworks at his confirmation hearings. Conservative groups are focusing on his statements on the issue, including those opposing tying increased emigration of Soviet Jews to a relaxation of trade barriers.

Kempton B. Jenkins, Armco's chief Washington representative who has worked with Verity on this issue, said Verity favors an increase in Jewish emigration but believes the law linking it to trade has become counterproductive.

Verity's background as a steel corporation executive has prompted some critics to question whether the head of a company in an industry that has lost its competitive edge to foreign suppliers is qualified to improve U.S. competitiveness.

Some critics question whether Verity will be able to participate fully in important administration policy debates about the future role of the steel industry and the continuation of steel import curbs beyond 1989.

But Verity can claim a family role in the rebuilding of one of the United States' major industrial competitors. His father was a colonel on the staff of Gen. Douglas McArthur and played a major part in the resurrection of the Japanese steel industry from the ashes of World War II.

Verity used his position as president of the U.S. Chamber of Commerce in 1980 to urge that American business executives take a greater interest in politics and government. He pushed all Armco employes, retired workers and stockholders to donate time and money to the political process out of a belief, stated in a Washington Post interview, that Congress has "put so many roadblocks in front of business that we've lost our competitive edge."

Verity is a keen competitor on the tennis and golf circuit as well as in the corporate arena. He and his wife, Peggy, play a mean tennis game, friends here said, and he was a champion golfer at Yale.

He was a major benefactor in the restoration of Ford's Theater, serving as board chairman in 1981 when a gala benefit drew President Reagan to the theater where President Lincoln was shot. Joy Baker, wife of White House chief of staff Howard Baker, who was then Senate majority leader, was an organizer of the gala.