John W. Warner, who was selected yesterday to replace the late Richard D. Obenshain as the Virginia Republican Party's nominee for the U.S. Senate, could be called the Horatio Alger of the Jet Set. Now 51, Warner went from being a high school dropout to a top Washington law firm, from an enlisted man to secretary of the Navy, and from a doctor's son who went through college on the GI bill to the husband of two wealthy and celebrated women.

Since losing the nomination to Obenshain at the GOP convention June 3, Warner has spent much of his time lending his name and the presence of his famous second wife, Elizabeth Taylor, to political fund-raisers and pondering the future. He and Taylor were preparing to leave on a long European vacation when Obenshain was killed in a plane crash Aug. 2.

Warner's second place finish at the convention, where he lost to Obenshain by 37 votes on the sixth ballot, was an impressive showing for some one new to Virginia politics. Stressing his experience in the Defense Department, as head of the American Revolution Bicentennial Administration and his credentials as a lawyer and farmer of two vast estates in Virginia horse country, Warner campaigned vigorously before the convention and managed to attract a large force, many of them new-comers, to the convention. The convention was billed as the largest political meeting ever held in the country, and certainly was the largest ever in Virginia. Money for Campaign

In a sense Warner, who opposes the Equal Rights Amendment, owes much of his success to his wives. His divorce from his first wife, heiress Catherine Mellon, gave him the financial security that allowed him to pump $561,571, mostly in borrowed money, into his preconvention campaign, twice as much as his two principal opponents.Elizabeth Taylor has served as a phenomenal attraction in getting people to Republican functions, allowing her husband to pick up political IOUs both for campaigning for Gov. John N. Dalton and for raising money for the party and the Dalton campaign.

In speeches and interviews, Warner spoke of his experience in government, starting as an assistant U.S. attorney in Washington and including his jobs. He has been called intelligent and persuasive. ARBA. Warner has listed his occupation as "cattle farmer" but has spent the bulk of his time campaigning. He logged 20,000 miles traveling around Virginia for Dalton, by his estimates.

Assessments of Warner's professional skills vary. "He combines a sharp mind with a warm personal touch," said former U.S. representative Joel T. Broyhill, Warner's campaign chairman.

". . . John Warner was a secretary who bent with every political breeze that blew," wrote Adm. Elmo R. Zumwalt, who served as chief of naval operations while Warner was secretary of the Navy. Warner was ". . . unhelpful to me in just about every way a secretary of the Navy could be unhelpful to the chief of naval operations in handling the racial dealing with contractors . . . I had long since adopted the policy of not relying on his assistance in any serious enterprise." Zumwalt Bid Failed

Ironically. Zumwalt (who wrote those comments in his book, "On Watch.") made an unsuccessful bid for a Virginia Senate seat in 1976, losing to Sen. Harry F. Byrd Jr. (I.Va.) Zumwalt's campaign was marked by financial troubles and Democratic Party disorganization.

But with Warner, the Republicans can expect a well-financed, media-wise campaign certain to cause concern among the Republicans.

"I've had 14 years of training and experience for this position." Warner is fond of saying, "I will not require on-the-job training."

His silver hair looks dark in photographs, combining with his smile to create a somewhat boyish effect. Early in his campaign he underwent a thorough physical examiniation at the University of Virginia and released the results to the press. (His health was called excellent). Concerned about his weight, he plays squash when in town. He has a house in Georgetown next to his former wife's home and occasionally runs for a mile or two while on the road campaigning.

He loves the colors red, white and blue. His ties, shirts and suits follow that theme. His campaign colors are red, white and blue, the engagement ring he gave Taylor is red, white and blue

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He also wears a copper bracelet which he describes as a 25-cent piece of wire that "makes me feel better," although he says there is no scientific reason why it should. Conservation Stressed

Warner presents himself as a moderate conservative leaning more to the conservation than the moderate. He says he would have voted against the Panama Canal treaties, and he favors increasing the country's defense capability. He says inflation and taxes are the primary concerns of the voters. He supports cutbacks in the federal bureaucracy (except Defense), and has urged President Carter to cut his staff salaries by 10 percent. Warner also support a proposal to prevent taxpayers who get a cost-of-living wage increase from being put into a high tax bracket because of that increase.

Warner's association with the Republican Pary goes back to his childhood. Although he lived in Washington and Northern Virginia, Warner's late father voted in Amherst, Va. - 160 miles southwest of Washington - and was a Republican in a Democratic-dominated state. In 1960 Warner worked in Richard M. Nixon's unsuccessful presidential campaign as a speechwriter and advance man, having earlier been a campaign volunteer for Dwight D. Eisenhower.

He headed Nixon's "Volunteers for Nixon" in 1968 and worked on the Nixon transition team after the election. He campaigned for Ford aud was chairman of Dalton's Fauquier County delegation to the 1977 state Republican convention.

But while emphasizing his political and professional experience. Warner is not naive about the special advantage he has in both his access to big money and the publicty value of his wife. "Most of the voters make up their minds in the last three days of the campaign," he told a delegate to the state convention. "What they do is follow the media. Think of that when you're considering another candidate."