President Reagan yesterday sent Congress three education bills that would help parents finance private school and college costs and impose more stringent eligibility standards for college students seeking federal grants and loans.

He proposed establishing tax-free education savings accounts for parents saving for their children's college expenses. He also seeks a voucher system that would enable parents who earn less than a certain income to receive their share of federal funds that would go to public schools and use the money to send their children to private or public schools of their choice. The third proposal would require all students applying for college grants and loans to demonstrate need.

The maximum funding for a student under federal grants and loans would be raised from $1,800 to $3,000, but students receiving the so-called Pell grants would be required to contribute 40 percent of their own educational costs.

In addition, all students in the Guaranteed Student Loan program would be required to demonstrate need. Currently just those from families with an annual income of $30,000 or more have to show need. And the fee for graduate students who borrow from student loan programs would be increased from 5 to 10 percent a year.

In a cover letter to Congress, Reagan said the changes in the rules for undergraduate and graduate student aid are being proposed because college costs are rising. This makes it more difficult for low- and middle-income students to attend college while "more affluent families who could contribute more have been paying a smaller share . . . relying instead on increasingly generous federal aid," he said.

To help students earn more money and qualify for the grants, he proposes expanding the Work Study program by 60 percent, to $850 million.

The proposed voucher system would, if local school boards agree, give parents of poor children the federal money now sent directly to local public school districts. The parents would then be free to use the money at any public or private school they choose. The education savings accounts program would enable parents to save as much as $1,000 per year for each child's college education with no income tax on interest.

These programs, combined with the recent proposal of tuition tax credits of up to $300 per year for students attending private or parochial schools, complete Reagan's education legislation package. It reflects his philosophy of lessening the federal role in education and enabling parents to send their children to private schools as an alternative to sometimes troubled public schools. In his radio address last Saturday, Reagan said that by giving parents more choice in where to send their children to school the public schools will be prodded to improve or risk losing their students.

In his letter yesterday, Reagan added that the three proposals he made yesterday will "bring parental choice and the benefits of competition to elementary and secondary education."

Terrel H. Bell, secretary of education, in a briefing on the bills, said they should not be construed as an attack on the public schools. "I feel that we need a little more of the philosophy of the marketplace in education," said Bell, noting that he has a daughter in Arlington public schools.