Andrew Pickens Miller grew up on a 70-acre farm in suburban Washington. His father, a State Department lawyer, was something of a rebel and the man who mounted the first serious challenge to Virginia's entrenched Byrd organization.

His mother was a Washington correspondent for the London Economist whose houseguests included progressive Henry V. Wallace and theologian Reinhold Niebuhr.

By birthright there are those who argue that Miller, currently seeking the Democratic nomination for governor of Virginia, should be what his father was 28 years ago when he sought the same office: a liberal, a witty speaker with a vision of world and national affairs, and a man with a precise, clearly enunciated philosophy. Yet Miller is none of these.

He is, by all accounts, an orthodox moderate by Virginia standards, a conservative by Washington standards, given to somewhat wooden speeches, fascinated by state government and a man who once told a friend he didn't understand "why in the world" the friend would consider leaving Richmond for Washington.

But Miller is also studious, aggressive, ambitious, "smart as hell" in the words of one Justice Department lawyer who has opposed him, and - unless most Virginia politicans are wrong - the current favorite in the June 14 primary.

At 44, Miller, a Virginia attorney general for almost eight years, is running the best financed primary campaign in the state's history against a man who is regarded as one of the best campaigners in the state, Henry E. Howell.

In a state that has shown a decided preference in recent years for conservative and Republican candidates, Miller likes to remind his audiences that he is "the only living Democrat" who has been elected as a Democrat to statewide office in Virginia since 1966.

His gubernational campaign is carefully conceived. It is painstakingly organized around the image of Princeton-educated Miller as a man well schooled in Virginia government and one who is capable of doing what Howell has been unable to do in his recent races: win. That promise - that a moderate Miller can win what a liberal Howell cannot - seems to provide the basis for more of Miller's support than any specific issue the campaign has raised.

"A lot of people are saying that they have been to the well for Henry many times and this time they want to elect a governor," said Emilie Miller (no relation), head of the Fairfax County Democratic Party.

Miller speaks much the same theme, telling would-be voters that he represents "a new generation of state leadership" that promises "better government, not more government . . . action, not words."

His stands on some other key issues are equally conservative. Unlike Howell, he opposes collective bargaining for public employees in the state, would fight strongly any effort to repeal the state's right-to-work law prohibiting compulsory union membership, and opposes an immediate end to the controversial fuel - adjustment clause, which allows public utilities to bill customers for increased fuel costs. Howell says it should be junked but Miller claims such a step might cost customers savings from increased use of nuclear power.

But on a wide variety of other issues there is little apparent disagreement. Both Howell and Miller say they are opposed to any general tax increase during the next four years.

Pledges of more state attention to Northern Virginia come from both men. Each has promised to set up a regional office in the Washington suburbs and pledged that they would give financial support to construction of the Metro subway system into Virginia.

Increased roles for blacks and women in state government have been pledged by both men. Miller's efforts to woo both groups have been hurt by what his critics say are his past stands.

His efforts to get Virginia exempted from the federal Voting Rights Act of 1963 are resented by many black groups and some women have questioned his commitment to passage of the Equal Rights Amendment, repeatedly rejected by the Virginia General Assembly. Critics say a major factor in the 1974 defeat of the amendment, which would prohibit discrimination on the basis of sex, was a memo from Miller's office warning that the amendment coudl lead to "sex-blind" restrooms, college dormitories, and prisons. Miller has disavowed the memo as an unapproved draft prepared by one of his assistants.

In appearances before black groups, Miller has defended his filing of the lawsuit over the Voting Rights Act, which authorizes federal supervision over election procedures in states with a history of racial discrimination. Miller says he filed the suit after he was directed by the 1975 legislature to make such a challenge in the courts. However, as early as 1970 he was publicly urging a court challenge of various sections of the act.

Miller says that as attorney general from 1970 to early 1977 he often "had to grit my teeth and fight the best I could" for a state policy which he privately opposed. As the state's top lawyer, that was his responsibility, to defend the state's interest regardless of his personal beliefs, he said.

"He was attorney general 24 hours a day and that was his passion," said Walter A. Marston, a former member of Miller's legal staff who is running his current campaign.

Indeed, those who know Miller claim that what many see as his somewhat distant personality is a product of his total immersion in his work. "He's a perfectionist in many, many ways," said Randolph W. Church, a Fairfax County lawyer who has known Miller since his law school days at the University of Virginia. "He demands a lot of his staff and he doesn't like a screwup. He's impatient with those whose minds don't seem to operate as fast as he does."

Others, including former Gov. Linwood Holton, a Republican whose term coincided with Miller's first four years as attorney general, disagreed. "Miller is something of a cold fish, as everyone knows," Holton said recently.

Even among his friends there is wide disagreement on what Miller's political philosophy is. "He's much more conservative than he appears," confided one former associate. "He's pretty pragmatic and certainly not a conservative in the Virginia sense," countered Church.

Many suggest that Miller has no overriding political philosophy; that he is, in campaign manager Marston's words, "basically a pragmatist." Justice Department antitrust lawyer John T. Shenefield tends to support that view."I think Andrew has come to the conclusion that having a strong political philosophy is pretty much of a luxury," he said. Shenefield sees Miller as "a moderate Democrat ready to take a step at a time."

Longtime friends say such an approach would be typical of the way Miller has acted over the years. At Princeton University, Miller majored in European history and wrote his senior thesis on the fall of the shortlived Russian government of Alexander Kerensky in 1917. Kerensky's fall, Miller said the other day, was inevitable. "The building blocks were not there." he said.

If nothing else marks his current campaign, it is clearly his "building blocks" approach to running. Some friends say Miller has "spent most of his life preparing to be governor," carefully building friendships, gaining knowledge that would boost him into the office.

His current staff of about 38 paid workers began building Miller's current organization 16 months ago when the first paid staffer went to work in a small downtown Richmond office. The first layer was a campaign finance structure that is expected to raise close to $1 million for Miller in the primary. Later came an organization that is devoted to turning out a large vote for Miller on June 14. The organization's goal is to contact every registered voter in the state prior to the primary, a task believed unprecedented in recent Virginia politics.

According to his critics, Miller took the same "bureaucratic" approach to running the state attorney general's office, quadrupling the small staff of 21 lawyers he inherited in 1970 to a force of 84 by the time he left office. Both Howell and John N. Dalton, the Republican nominee for governor, have condemned the staff expansion, saying "we can't afford that much government."

Miller defends the growth of his staff, saying it was prompted by a huge shift in enforcement responsibilities for pollution and job safety rules from the federal government to state governments. It was also caused by a deliberate decision to end the state's policy of farming out legal tasks to favored law firms across the state, a form of political patronage long condemned by Virginia Republicans.

Miller vigorously defends the opinions his office issue - all 3,887 of them - saying the Virginia Supreme Court never overturned one of them while he was in office.

Miller says he is not a wealthy man. His assets, according to a disclosure form filed with state officials, consist of a two-story brick home in suburban Richmond, a parcel of undeveloped land in Prince William County, and common stocks in a half-dozen corporations. Altogether Miller has said his net worth is "slightly over $200,000." The amount has fallen slightly since he left his $37,500-a-year job as attorney general in January, he says. Much of his wealth apparently stems from his nine years as a lawyer in the southwest Virginia town of Abington where he developed a reputation as one of the region's best trial lawyers before he ran for attorney general in 1969.

The Miller family lived in a large stone farmhouse about 15 miles west of Washington near the northern edge of what is now Fairfax City until Miller was 16 years old. At that time the elder Miller decided to move to Charlottesville in the hope he could better run his campaign against the Byrd organization from there.

Hostility toward the elder Miller for his refusal to bow to the Byrd organization was strong in some portions of Northern Virginia at the time. Miller's mother, who now lives with Miller's father on the North Carolina Outer Banks, can recall Andrew and his brother being literally chased out of some Fairfax stores when they asked permission to hang one of their father's posters in the store.

Candidate Miller said he can't recall that incident, but he acknowledges that he owes his parent much for the "very high standards and commitment" they urged him to devote to any undertaking.

Why did he choose state government instead of a national arena? Virginia, Miller said, is "where I thought I could make the greatest impact . . . Besides, I don't take a large stageto play on."