HOUSTON, OCT. 29 -- The six Republicans who would like to succeed President Reagan found just one thing to really argue about at their first debate: a prospective arms control treaty that Reagan views as potentially one of his greatest triumphs.

It was a strange topic to open the campaign to become Reagan's successor. Many polls show that the American public largely supports the prospective treaty to eliminate medium-range and shorter-range nuclear missiles in Europe, and it is widely believed that a summit at which Reagan signs the accord would help restore some vitality to his troubled presidency.

Yet it was the only topic on which Republicans stalking front-runner Vice President Bush picked a fight in the first GOP showdown here, which was broadcast by the Public Broadcasting Service. With the exception of the arms control exchange, in which Bush was the only unqualified supporter of the treaty, most of the candidates preened for points on style rather than picked knock-out fights on major issues.

"They would all be different presidents, but the issues are not that different. It's more style," said Ed Rollins, campaign manager for Rep. Jack Kemp (R-N.Y.) and a former Reagan political adviser.

Even the most provocative contender, former Delaware governor Pierre S. (Pete) du Pont IV -- who injected Social Security into the debate to the others' discomfort and who aimed the sharpest attack on Bush -- wound up getting the lowest marks in a poll of Republican debate-watchers released here today.

The Republicans had nothing to say on the Iran-contra affair, which only a few months ago appeared to be a major handicap for Bush. Nor did they say much about support for the Nicaraguan contras, which Reagan is battling to sustain, or the growing U.S. military presence in the Persian Gulf. And only du Pont mentioned the failed effort to put Judge Robert H. Bork on the Supreme Court.

Even differences on economic policy were described in gentle tones, despite the stock market collapse last week. Instead of arguing about specific tax and spending remedies, the candidates choose to discuss whether it is a good idea to have budget negotiations with the Democrats. Bush and Sen. Robert J. Dole approved; Kemp said "I don't think there's any kind of a budget deal you can make with {House Speaker} Jim Wright that's going to be an advantage . . ."

The debate's message seemed to be that the Republican candidates -- with the exception of du Pont -- wanted to be on their best behavior and decided in advance to save brawling for later. Here's how they approached the problems of style and themes:Bush: Wanted to avoid awkward gaffes or angry outbursts -- and he was successful -- while emphasizing his loyalty to Reagan. Instead of getting rattled by du Pont, Bush, who has often been ridiculed for his establishment upbringing, put down du Pont with a firm "Pierre, my friend, Pierre . . ." In a survey after the debate of 400 self-identified Republican primary voters in 13 key early primary states by SRI Research Center Inc., Bush received the highest overall marks: 64 percent said he would be the GOP nominee.

Dole: Wanted to come across as the steady Washington insider, rather than the slashing campaigner of earlier years, and succeeded by taking a gently humorous approach. "He wasn't flamboyant and he didn't intend to be flamboyant," said Dole strategist David Keene. "We didn't think in this debate it was our task or our need to take on George Bush." The low-key approach had its risks, too: the poll found that few GOP viewers thought Dole improved his standing.

Du Pont: Wanted to be different, and was, challenging the others to discuss one of the greatest taboos in GOP politics -- Social Security financing -- and goading Bush by saying he had not seen "any vision, any principles, any policy." But du Pont reaped only a backlash in the hall. And the poll reflected that: He tied with Alexander M. Haig Jr. for the worst marks.

Haig: Wanted to shed the image of a stern military man, saying at the outset that generals had not led the nation into war when they became presidents. Haig seemed more cool and measured than in his earlier days in the Reagan presidency, when many remembered his malaprops and quick temper. Haig matched Bush for highest marks on foreign policy expertise in the poll, but did not gain much overall.

Kemp: Wanted to portray himself as a candidate of vision, stressing his support for the Strategic Defense Initiative and tax cuts, and avoiding rigid focus on international monetary policy, a favorite subject in the past. Kemp stuck by his supply-side views that tax cuts are more important than deficit reduction. He dismissed the widely held belief that U.S. deficits were responsible for the stock market's collapse. Kemp scored well on economic points in the poll.

Marion G. (Pat) Robertson: After touching off an uproar recently with a remark widely interpreted as criticism of First Lady Nancy Reagan, the former television evangelist tried to turn on the charm. The poll showed him far exceeding public expectations. Aides were happy with the outcome, saying he had played in the mainstream and won plaudits for recruiting Democrats into the GOP. "I came off as I know I am . . . reasonable, comfortable," Robertson said. "And not as some strange person."