The 96th Congress convened yesterday with the House adopting -- over Republican objections -- a set of new rules designed to cut down the number of floor votes and the time spent voting.

The Senate, for its part, took up a proposed revision of its filibuster rules, while Senate Republicans installed a generally moderate group in several contested leadership positions. (Details on page A6.)

The new House rules are a response to the increase in recent years in the volume of legislation; there are so many bills the House can no longer easily handle them all.

The Democratic leaders also rammed through some rules changes to help them deal with this year's expected rush to cut the budget. They changed the congressional budget process so that members will no longer be able to propose cuts without specifying where they should come, and so that senior and presumably steady members will be able to stay on the Budget Committee, rather than have to rotate off.

The key vote on adopting the rules was 241 to 156, along strict party lines.

Preceding the rules fight were the traditional rites of the opening day. The galleries were packed with families and well-wishers, and the floor abounded in children allowed there to watch the mass swearing-in of new and old members. The election of Republican and Democratic leaders produced the usual good natured joshing and to the surusual good natured joshing and to the surprise of no one, Thomas P. (T-p) O'Neill Jr. (D-Mass.) defeated John J. Rhodes (R-Ariz.) for speaker by 269 to 152.

Rhodes, reelected minority leader, noted that many Democrats had campaigned on a platform of fiscal conservatism, and offered O'Neill a copy of the Republican legislative agenda to help him construct what Rhodes called "this Republican Congress" made up of "one terrible lot of Democrats."

O'Neill, in accepting the speaker-ship, pledged to work for "income tax dollars well spent," to "control inflation without intolerably high unemployment," for "health care without a big budget deficit," and to "control special-interest money in campaigns."

The rules fight highlighted what will be the last meaningful floor session for awhile, as Democrats and Republicans dissolve into party caucuses to fill important vacancies on key committees and elect committee and subcommittee chairmen.

Democrats pushed through rules which changed from 20 to 25 the number of members needed to get a recorded vote on an amendment, which permit the speaker to put off for a day and cluster votes on bills, which do away with certain procedural votes and which cut down from 15 minutes to five minutes the time allotted for voting on certain motions.

Majority Leader Jim Wright (D-Tex.) called the changes "modest,' with the purpose of facilitating and expediting the business of the House.

Republicans objected not only to the rules changes themselves but also to the take-it-or-leave-it manner in which the Democrats put them through, allowing for no amendments to their package.

While the major part of the rules package was adopted yesterday, the rules fight is not entirely over. The Democratic Caucus must still consider next week some important pending changes dealing with ethics questions. One change would require a caucus vote on indicted chairmen, such as Rep. Daniel J. Flood (D-Pa.), whose bribery trial started yesterday, causing him to miss part of the opening of Congress.

Another would require an automatic motion to expel a member convicted and sentenced to more than two years once his appeals are exhausted, and another proposal would prohibit a convicted member from voting even though he was reelected.

These changes would affect Rep Charles C. Diggs Jr. (D-Mich.), convicted and sentenced for taking salary kickbacks.

At their December caucus, Democrats' enthusiasm for such proposals appeared to be waning. But yesterday, Republican freshmen took up the ethics reform issue by trying to push a move to require that any member censured, reprimanded, or convicted be prohibited from holding a committee or subcommittee chairmanship or ranking membership for more than two years after the action against him. Republican leaders deflected the move in their pre-session caucus by referring the proposal by freshman William Dannemeyer (R-Calif.) to a research committee for a study. But the vote was a close 42 to 40.

Meanwhile, a proposal for partial public financing of House general elections was given the symbolic designation of H.R. 1 by Speaker O'Neill. At a press conference, the principal sponsors, Reps. John Anderson (R-Ill.), Thomas Foley (D-Wash.), Barber Conable (R-N.Y.), Abner Mikva (D-Ill.) and Morris Udall (D-Ariz.), predicted they would win the eight-year-old struggle for public financing.

They cited a Democratic Study Group survey which showed that more than 80 members spent over $200,000 this year and six members spent over half a million dollars on their races.

Udall said public financing was necessary to counter the trend of specialinterest groups with narrowly based goals overly influencing Congress. He said it would allow candidates to have broad support that would deflect the influence of such groups.