Senate Republicans yesterday chose Sen. Howard H. Baker Jr. (Tenn.) as majority leader for the 97th Congress, suppressing their differences in favor of an ideologically balanced but western-dominated cadre of party leaders.

A moderate among conservatives in the new Republican majority, Baker will be the only party leader from east of the Mississipii River when the Senate reconvenes in January under GOP control for the first time in a quarter century.

Baker's unchallenged elevation from minority leader to majority leader came as the lame-duck session of the 96th Congress began to sputter toward an anticipated end this weekend, with the Senate putting on an especially bizarre display of back-to-back filibusters on fair housing legislation and a judgeship dispute.

As for Senate Democrats, it was a time for musical chairs as several prominent committee chairmen opted to claim seniority as ranking minority members on committees other than the ones they headed in the current Congress. mAmong them was Sen. Edward M. Kennedy (Mass.), who will serve as ranking Democrat on Labor and Human Resources rather than Judiciary, which he now heads.

The House, meanwhile, passed and sent to the Senate last-minute legislation sought by the auto industry authorizing negotiations to limit future imports of Japanese cars and light trucks.

In the only contested Senate Republican race, conservative James A. McClure (Idaho) defeated moderate John Heinz (Pa.) to head the Republican Conference, the caucus of all GOP senators.

Ideology and region appeared to play a part as the Republicans voted 33 to 20 for McClure despite Heinz's role, as current chairman of the Republican Senatorial Campaign Committee, in helping orchestrate the party's stunning Senate victories at the polls last month.

In the only other race for which a contest had been expected, Bob Packwood (Ore.) was elected without opposition to take over as campaign committee chairman after Bob Dole (Kan.) dropped out of the race at the last minute, apparently for lack of votes. Packwood, a moderate with friends in conservative ranks, apparently locked up the race from the start.

As the 53 incumbent and freshly elected Republican senators gathered in a buoyant mood in the historic Old Senate Chamber on the first floor of the Capitol to elect their new leaders, they actually made few changes in the old leadership. Minority Whip Ted Stevens (Alaska), who is generally regarded as a moderate, will now assume the second-ranking leadership post. Conservative John Tower (Tex.) was re-elected to the third post as chairman of the Republican Policy Committee. Another conservative, Jake Garn (Utah), will continue as secretary of the Republican Conference.

In addition, as the most senior Republican in the Senate, Strom Turmond (S.C.), will serve in the largely honorary post as president pro tempore of the Senate, which makes him third in line for the presidency behind the vice president and the speaker of the House.

As majority leader, Baker will succeed Robert C. Byrd (W.Va.) who is expected to be elected the Democrats' minority leader either this week or when Congress reconvenes in January.

Early talk that conservatives might challenge Baker, who had made a futile early bid for the presidential nomination last winter, was headed off from the start by President-elect Ronald Reagan and his chief lieutenant in Congress, Sen. Paul Laxalt (Nev.), who also was his campaign manager.

In the same spirit, Baker -- smiling broadly at a press conference after the closed-door Republican caucus yesterday -- promised both strong support for Reagan's programs and some changes in the Senate.

"I intend to try to help Ronald Reagan [carry out] the commitments he made during the campaign," said the 55-year-old, three-term Tennessee senator, predicting more executive-legislative cooperation than the country has seen in years.

As for the Senate, Baker said he would like to see it stop acting "like a bunch of elected bureaucrats passing thousand-page bills" and return to its earlier role as a "forum for discussion of important issues . . . a great debating institution."

On the Democratic side, other senators will be switching leadership roles on committess. Harrison A. Williams Jr. (N.J.) will take over as ranking minority member on the Banking Committee. William Proxmire (Wis.) will move his seniority from Banking to Appropriations. Joseph R. Biden Jr. (Del.) will become ranking Democrat on Judiciary.