In his first major speech since taking office, Education Secretary William J. Bennett called yesterday for America's schools to expand beyond teaching the traditional "three R's" of reading, writing and arithmetic and to embrace what he called "the three C's -- content, character and choice."

Bennett used the occasion, a luncheon address at the National Press Club, to promote some of the Reagan administration's politically sensitive education proposals, including school prayer, education vouchers and tuition tax credits for parents who send their children to private schools.

"Might not voluntary school prayer be an auxiliary to character in some places?" he asked.

Bennett rejected the 1960s idea of value-neutral classroom curricula and called instead for schools in the 1980s to teach "thoughtfulness, fidelity, kindness, honesty, respect for law, standards of right and wrong, diligence, fairness and self-discipline."

In support of vouchers and tax credits -- which face an uncertain fate in Congress this year -- Bennett said the states should be "the laboratories of experimentation."

He cited Minnesota's tuition tax deduction and an unusual proposal by Gov. Rudy G. Perpich in that state to provide high school juniors and seniors with vouchers to attend the public schools of their choice, regardless of jurisdiction.

But proposals for tuition tax credits and vouchers have not been as popular in another state, Louisiana, where on Saturday an Education Department official withdrew as a conference keynoter rather than "self-censor" his speech supporting those two controversial concepts.

John D. Klenk, director of planning and evaluation in the department, was asked not to talk about vouchers and tuition tax credits by organizers of a conference on parental involvement in schools.

Bennett in a statement yesterday said he was "indignant and dismayed" by that action.

In yesterday's speech, Bennett called for a return to a traditional content. Bennett cited such American classics as Huckleberry Finn and Treasure Island as the kind of book students should be reading.

"They should know where the Amazon flows, and what the First Amendment means," he said.

"They should know about the Donner party and slavery, and Shylock and Hercules and Abigail Adams, where Ethiopia is, and why there is a Berlin Wall," he said.

Department officials billed yesterday's speech as the launching of the administration's education agenda for the next four years.

But the agenda was a limited one, short on specific proposals and appearing cognizant of the political reality that state capitals -- not the federal Education Department -- are the primary arenas for most changes in education.