President Reagan is the overwhelming choice of Republican voters in New Hampshire, and Walter F. Mondale has a substantial lead over his competitors among Democratic voters, according to a new poll of voters in the nation's first primary state.

Reagan was the preference of 59 percent of the GOP respondents, followed by Vice President Bush with 15 percent, Senate Majority Leader Howard H. Baker Jr. (Tenn.) with 6 percent, Rep. Jack Kemp (N.Y.) with 2.5 percent, Sen. Robert J. Dole (Kan.) with 1.5 percent, Sen. Jesse Helms (N.C.) with 1 percent and the rest undecided. About 65 percent of the Republicans wanted Reagan to run for reelection.

Among Democrats, Mondale had 43 percent, Sen. John Glenn (Ohio) 22 percent, Sen. Gary Hart (Colo.) 7 percent, Sen. Alan Cranston (Calif.) 3.5 percent, former Florida governor Reubin Askew 1 percent, Sens. Dale Bumpers (Ark.) and Ernest F. Hollings (S.C.) 0.5 percent each, with 22.5 percent undecided.

As might be expected, Democrats were substantially more in favor of increasing domestic spending and cutting the defense budget than Republicans. Nearly half the Democratic respondents, 47.5 percent, thought defense spending should be cut, while 16.5 percent thought it should be increased. Of the Republicans, 33 percent favored more military spending, 28 percent thought it should be cut and the rest thought the current level was about right.

The survey of 1,007 New Hampshire voters--440 Republicans, 340 Democrats, the rest Independents--was taken by the Marist College Institute for Public Opinion in Poughkeepsie, N.Y.