Jimmy Carter began his campaign for reelection today where presidential campaigns always begin - the nation's first primary state.

Carter arrived here this afternoon with all the trappings of the presidency, fresh from delivering a somber speech to an audience in a prestigious New York City hotel on the perils of the nuclear arms race.

But here, he was plunged immediately into the carnival-like atmosphere of presidential politics, complete with a high school brass band that greeted him at Pease Air Force Base with a blaring rendition of "Hail to the Chief."

A few minutes later, the president found himself on the stage of a high school auditorium answering questions about clean water, federal funding of education programs and the availability of mortgage money.

There were even a couple of hecklers-shouting complaints about nuclear power-to make the campaign scene complete.

Tonight, Carter flew to Bedford, where at a state Democratic Party dinner he delivered a highly partisan speech, denouncing "Republican economics," claiming that this "Democratic economics" had cut the unemployment rate in New Hampshire in half and promising that he will "refuse to play politics with the economic health of the United States."

In both Portsmouth and Bedford, Carter plugged for his opposed "windfall profits" tax on the oil industry and appealed for patience, understanding and support in his flight against his most pervasive and serious political problem-inflation.

"All of you know how bad it is, and it will not get much better in the near future," the president said of inflation in Portsmouth. "I'm not going to kid you about this. We are going to see rising price figures coming out week after week for the next few months.

"The inflation we have today has been gaining momentum for more than a decade. It can't be halted overnight because it has seeped into the fabric of our economy. There is no easy solution to it and, frankly, anyone who says there is an easy solution is either a liar or a fool."

Carter thus revealed what is expected to be his tack in dealing with inflation, at least until there is better economic news-that he is doing the best he can and no one else could do better.

Ten months from now, New Hampshire, as always, will be the battleground of the first presidential primary-a highly publicized testing of an incumbent president's standing in his fourth year in office. Carter has not officially announced that he will run for reelection, but he has formed a campaign committee and there was no question today that this was his first reelection campaign trip.

Almost immediately after arriving here, the president also displayed his willingness to use the advantages of incumbency. He announced that he has ordered the Department of Energy to ensure by October that there is a reservoir of 240 million barrels of home heating fuels, a vital resource in the bitter, New England winters.

White House press secretary Jody Powell said that inventories of home heating fuels now stand at 110 million barrels and should be at least 140 million barrels.

Carter also told the town meeting that it was "a very sad mistake" for the House Commerce Committee to reject his standby gasoline rationing plan. Powell told reporters that if the rejection stands, the country will be in "a God-awful situation" if rationing becomes necessary.

Throughout his stay in New Hampshire, the president, appearing relaxed and confident, seemed to be in mid-campaign form. He told a young girl who asked him if his daughter, Amy, "bragged" about being the president's offspring that, no, Amy more often had to "apologize" for it. He followed up by inviting the somewhat bewildered child to visit him and Amy at the White House.

About all that marred the president's visit to New Hampshire was the presence of a handful of antinuclearpower hecklers, one of whom shouted "liar" to Carter's comments on the subject at the Portsmouth town meeting.

In Bedford tonight, Carter appealed for support for the strategic arms limitation treaty-the subject of his New York speech-and returned to the campaign themes that served him so well in 1976.

"Here in New Hampshire, I promised you a government as good as the people," he said. "Some critics dismissed that as meaningless rhetoric. But you understood what I was talking about."

White House officials made no attempt to disguise the political nature of the New Hampshire visit. Asked why the president chose to come to New Hampshire from New York one member of the presidential entourage said, "Better than goint to Arizona. They don't have a primary." CAPTION: Picture 1, The president sheds his coat, later rolling up his sleeves, as he fields questions on various domestic issues at town meeting at Portsmouth High School. AP; Picture 2, At Portsmouth; "We are going the see rising price figures . . . week after week . . ." UPI