A presidential campaign presents a choice for the nation, a challenge for the contestants -- and an opportunity or affliction for hundreds of other politicians.

Connecticut, a small, closely contested state, is a laboratory study of the ways in which dozens of private political agendas being pursued by candidates, campaign consultants and party officials have to be blended or thwarted by those who are managing the presidential cmapaigns.

Although it has only eight electoral votes, Connecticut is a top-priority state for both the Republicans and the Democrats -- and one of the strongest states for independent John B. Anderson.

Jimmy Carter lost the state narrowly -- 53 to 47 percent -- in 1976 and was beaten in the March primary this year by Sen. Edward M. Kennedy. But since Ronald Reagan also lost the primary here this spring (to his present running mate, George Bush) the Carter camp rates Connecticut -- along with Michigan -- as one of the two best bets in the country to shift electoral votes from the Republican to the Democratic column. Recent polls show Carter and Reagan almost even, in the high 30s, with Anderson holding almost 20 percent of the vote.

In addition to being a major presidential battleground, Connecticut has a standout Senate race, with Rep. Christopher Dodd (D) opposing former New York senator James L. Buckley, a conservative Republican, for the seat of retiring Democrat Abraham A. Ribocoff.

And here in New Haven, two highly regarded products of the state senate, Democrat Joe Lieberman and Republican Larry DeNardis, are locked in a tight race for the seat being vacated by retiring House Budget Committee Chairman Robert Giaimo (D).

Interlocking with and cross-cutting these visible contests are a great many private-agenda items, ranging from conventional to bizarre.

Take Connecticut's ranking Republican official, Sen. Lowell P. Weicker Jr. Last week, Weicker endorsed Reagan for president, although he had called him "simple-minded" two months ago. But Weicker refuses to endorse Bush for vice presient, perpetuating a youthful feud that had its origins in the wealthy suburb of Greenwich, where both of them grew up.

Last year, Weicker had to abandon his own presidential campaign when it failed to gain any support. Then just at the time Bush won the Iowa caucuses last January, Weicker publicized a charge that Bush had tried to conceal evidence of Watergate-era campaign finance hanky-panky -- a charge that Bush denied.

Although Bush is on the same lever of the voting machines with Reagan, Weicker said, "I would be a hypocrite to endorse him, knowing what I know he did."

While taking this high-minded stand on the top race, Weicker has proclaimed himself officially neutral in the Buckley-Dodd Senate contest. But this summer he encouraged an unsuccessful primary challenge to Buckley, declaring that "Buckley represents everything I have fought against in the Republican Party."

Buckley, in turn, describes Weicker's position as "Swedish neutrality" -- an echo of the silent hostility Sweden displayed toward the Axis during World War II.

Many Republican politicians in Hartford had expected the mercurial Weicker to bolt the party this fall -- to endorse Dodd and spurn Reagan. They speculate that the main reason he did the opposite was to keep open his option of running for reelection (or for governor) in 1982 as a Republican -- or as an independent, as he has sometimes threatened to do.

While the Weicker situation may seem enough for one party to have to contend with, it has not been the only -- or most vexatious -- problem for the Connecticut GOP. Until last week, there were no Reagan headquarters or campaign coordinator in the vital state, because of another private-agenda dispute, pitting the Republican state committee against Roger Stone, a conservative campaign consultant with great clout in the Reagan organization.

Stone, who made the original foray for Reagan into Connecticut back in the spring of 1979, acquired on that trip not only a fund-raiser for the campaign but also a partner-investor in the campaign consulting firm Stone and two others created in early 1980: Greenwich businessman Lee Hanley.

To Stone, who is running New York for the Reagan campaign and keeping an eye on the northeastern states, financial backer Hanley seemed a logical choice of the Reagan coordinator's job in Connecticut. But to Republican state chairman Ralph Capecelatro, Haley was a man without political experience who -- like others in earlier campaigns -- might run a narrowly focused effort for the presidential nominee and then leave the party organization to repair the damaged feelings when the presidential race was over.

Although Capecelatro himself was an early Reagan supporter in 1980 (after backing President Ford in 1976), Stone and others in the Reagan camp viewed the state committee as a nest of Bush backers refusing to acknowledge who had won the nomination.

From the end of the Republican convention in July until just last week, the tug-of-war over the coordinator's job continued, with neither side yielding -- and no Reagan headquarters operating in the state.

Then a compromise was reached, Mary Ann Knous, a neutral outsider, a New York professional known to Capecelatro and the Connecticut Republicans through her previous job as a regional field representative of the Republican National Committee, was brought in as coordinator -- with Hanley as one deputy and an early Bush supporter as the other.

"This ought to be a Reagan-Bush state," Knous said as she warily surveyed her new domain last week. The state carried for Bush (but) the country carried for Reagan and that's something the Reagan and Bush people both have got to get used to."

The Democrats have been too busy solving their own problems to enjoy the Republicans' miseries. Carter's primary defeat by Kennedy dramatized what many Democrats believe to be a chronic weakness for the president -- particularly among the Italian Catholics who comprise a key voting bloc here. The Kennedy victory also exacerbated the internal fighting between his supporters and such pro-Carter Democrats as Ribicoff, Gov. Ella Grasso and national committee treasure Peter Kelley.

When Ribicoff and Grasso took prominent public roles in quashing Kennedy's "open convention" naneuver at Madison Square Garden, four Connecticut Kennedy delegates -- all members of the machinists union -- walked out in protest.

The Carter forces were quicker than Reagan's to recognize the need for an outside peacemaker to run the fall campaign. They picked Patti Knox, a veteran Michigan polician with close ties to the United Auto Workers, which helped Kennedy in the primary but now supports Carter.

Grasso, who was embarrassed by Carter's loss in the primary, has put one of the her top aides, Dan Reese, fulltime in the Carter campaign. Carter to trying to ride on the governor's popularity in much the same way that the Reagan campaign is latching onto the home-grown strength of Bush, a Yale product whose father was once a senator from Connecticut.

Democratic campaign posters here show Carter and Grasso in a smiling handshake, the legend reading, "Partners in Victory."

"If the voters can't relate to Carter," Reese said, "they can at least relate to the Carter-Grasso relationship."

The Democrats in the House delegation, all of whom but Giaimo initially supported Kennedy, have now endorsed Carter. But there were painstaking negotiations, which climaxed only today, to bring into the campaign the most ambitious and influential of the "new guard" legislators, Rep. Toby Moffett.

The 36-year-old third-termer has given his contemporary, Chris Dodd, a clear shot at succeeding Ribicoff this year. But he has made known to all that he wants to run for govenor or senator in 1982.

After taking a conspicuous role in helping Kennedy win the Connecticut primary, Moffett further demonstrated his influence by helping a youthful long-shot, Samuel Gejdenson, defeat John N. Dempsey Jr. -- former state Democratic chairman, son of a former governor, and favorite of the state Democratic establishment -- for the nomination to the House seat Dodd is vacating.

Moffett's endorsement and organization have acquired considerable currency in Connecticut politics, and in recent weeks the congressman has not been shy about demonstrating his own recognition of their value -- and seeking to have his standing certified by the Carter campaign.

As Carter aides relate the story, Moffett told White House congressional liaison men at the end of the Democratic convention that Carter should invite him and other pro-Kennedy congressmen for a meeting as a prelude to their endorsement.

When First Lady Rosalynn Carter came to Hartford this month to launch the presidential campaign Moffett was put in the car with her and Gov. Grasso. By prearrangement Mrs. Carter invited him to see the president -- without the other 39 congressmen -- and Moffett accepted. When they met, Moffett formalized his support of Carter and said he would help the campaign on college campuses and with labor unions.

What he did not say, but what Carter campaign officials assert, was that he set a price on a full-scale effort by himself and his organization -- being named honorary co-chairman of Carter's Connecticut campaign, co-equal to the governor and the senior senator.

Moffett denies that he personally said any such thing to the president or first lady, but concedes that Carter campaign official might have received such an impression from their discussions with his top aide, Jeff Lictman. In any case, that was too high price for the Carter high command to pay, much as they wanted Moffett's help. Today it was announced that Moffett would be announced that Moffett would be co-chairman of the campaign steering committee along with Giaimo -- a step below Ribicoff and Grasso, but a step ahead od everybody else in the party hierarchy.

Carter's Connecticut managers were relieved at the compromise and somewhat amused at the negotiations. But no one involved seemed to blame Moffett for trying to get all he could from the situation.After all, presidential campaigns come along only once every four years, and a politician has to take his opportunities where he finds them.