Del. Eleanor Holmes Norton (D-D.C.) learned yesterday she will begin her career in Congress by looking after her own back yard.

Rep. Wayne T. Gilchrest (R-Md.) will spend the next two years watching over the country's waterways, and freshman Rep. James P. Moran Jr. (D-Va.) will keep an eye on the troubled banking industry.

The Washington region's three new House members found out yesterday how they will spend much of their time and energy through 1992 as they received their first committee assignments. The positions are awarded by the House leadership and determine the areas of legislation on which members will concentrate.

Getting the right committee assignment is also the first political test for congressional freshmen, who lobby hard for the panels of their choice. All three Washington area freshman passed by winning the positions they wanted most.

Norton was assigned to the Public Works and Transportation Committee and the District of Columbia Committee. Gilchrest was assigned to the Merchant Marine and Fisheries Committee and the Science, Space and Technology Committee. And Moran was assigned to the Banking, Finance and Urban Affairs Committee.

Not all commmittee assignments were decided yesterday, including the Post Office and Civil Service Committee on which Moran wants a spot. More appointments will be announced next week.

The three members said they think their assignments will benefit their districts, although in two cases the rewards will be indirect. Gilchrest's interest in the Merchant Marine Committee is the most obvious. He represents Maryland's 1st District, which includes 13 counties that front on the Atlantic Ocean or the Chesapeake Bay.

The assigment "is a step in the right direction," said Tony Caliquiri, Gilchrest's administrative assistant. "There was a fear during the campaign that a junior House member would not be able to get this assignment."

Norton said she chose Public Works as part of a strategy for horse-trading with other House members. Although as the District's delegate Norton cannot vote on the House floor, she can vote in committee. Public Works has jurisdiction over such pork barrel items as road projects that are sought after by many members.

"I need an increased federal payment for the District," she said. "Maybe we can work something out."

During the fall campaign, Moran accused his opponent, Rep. Stan Parris, of serving on the Banking Committee as a way to obtain political contributions from the banking industry.

Moran said recently he is interested in housing proposals that come before the committee and in banking industry reform.