Rep. Ronald V. Dellums (D-Calif.), setting a goal of making the District of Columbia "a showcase for what the inner city can truly become," assigned top priority yesterday to solving the capital city's pressing financial problems.

Dellums, taking over as chairman of the House District Committee, said he wants Congress to authorize the city to impose a commuter tax, to set a formula for calculating the annual federal payment to the city, to curtail congressional review of the city budget and to win federal support for more than $2 billion in unfunded city pensions.

In the long run, Dellums told reporters at a Capitol Hill news conference, he wants "a totally free and independent District of Columbia, one which will guarantee... the rights, responsibilities and representation guaranteed all... 50 states."

Declaring that a conservative tide is running in the nation, Dellums predicted it will take four or five years for the necessary 38 states to ratify the proposed constitutional amendment to grant the District full voting representation in both houses of Congress.

Dellums is one of two new House chairmen dealing with District affairs. The House Appropriations Committee tentatively chose Rep. Charles Wilson (D-Tex.) yesterday to be chairman of its subcommittee on the D.C. budget, succeeding veteran Rep. William H. Natcher (D-Ky.).

Natchr was chosen to be chairman of the Labor, Health, Education and Welfare Appropriations subcommittee. The Democratic caucus is expected to ratify Wilson's and Natcher's appointments today.

Under congressional procedure, Dellums' District committee acts on legislation authorizing expenditures, while Wilson's appropriations subcommittee reviews the requests and, in conjunction with its Senate counterpart, sets the level of the annual federal payment to help finance the city budget.

The federal payment this fiscal year is $235 million. President Carter has proposed $317 million for next year.

"The federal payment is not related to anything [objective]... it is a very political figure," Dellums said, calling for the adoption of a formula "to tie it to something predictable and real."

Dellums helped push a bill to provide $1.6 billion in long-term subsidies to the city's pension programs through Congress last year, only to see it vetoed by the president.

"We now have to meet with the president to see what terms he will support," Dellums said.

Dellums also said he supports action on such metropolitan problems as full funding for the Metro subway system and for dealing with the suburbs on such matters as water supply and sewage disposal.

He said the proposed transfer of St. Elizabeths Hospital from the U.S. government to the city should be contingent on continued adequate federal financial support.

Dellums, who succeeded Rep. Charles C. Diggs Jr. (D-Mich.) as committee chairman, said he did not like "to achieve status at the expense of anybody else's misery." Diggs is appealing his conviction last year of 29 counts of mail fraud and receiving salary kickbacks from his staff. He will remain a District committee member.

Dellums said he expects to assign the chairmanship of a subcommittee on D.C. finances to himself.Repeating what he said last week after a visit to the District Building, Dellums said he would move on the commuter tax whenever Mayor Marion Barry requests.

"If I were acting in a total vacuum," Dellums said, "I would push that bill very hard," giving the District tax-levying power equal to those of all states.

In a related matter, Barry met separately yesterday with Sen. Thomas F. Eagleton (D-Mo.), chairman of the Senate Governmental Affairs subcommittee on District affairs, and Sen. Charles McC. Mathias Jr. (R-Md.), the subcommittee's ranking minority member. Barry met last week with Sen. Patrick J. Leahy (D-Vt.), chairman of the D.C. Appropriations subcommittee.