CNN

WASHINGTON (CNN) - Most Americans say they are not concerned about the personal characteristics of the next Supreme Court justice - but they have very firm opinions about that person's experience and legal credentials, according to a new survey.

Nearly nine in ten Americans questioned in a CNN/Opinion Research Corporation poll released Monday say that it is important to them that President Obama's nominee for the high court have some experience as a judge. Experience in elected office is much less important - roughly half say it is important to have someone on the Court who has served in elected office, and half say that doesn't matter.

The public is much less concerned about gender or race. Ailing Justice Ruth Bader Ginsburg may be the only woman currently serving on the high court, but most Americans - including a majority of women - say it is not vital to for the president to nominate a woman to replace Justice David Souter. Sixty-one percent of those surveyed - 65 percent of men, and 58 percent of women - say it is not important for Obama to pick a woman. The sampling error on the question for all Americans is plus or minus 3 percentage points; for the results by gender, it is plus or minus 4.5 percentage points.

Fewer still say the race or ethnicity of the nominee is important. There are no Hispanics on the Supreme Court, but roughly three in four of those polled say it is not important for President Obama to name a Hispanic nominee. Nearly eight in 10 say it is not important to them that the nominee be black.

What about the issues that the next justice will tackle once he or she is elevated to the high court? Only three in ten Americans would like to see the Court overturn Roe v. Wade.

Ands state legislatures continue to pass legislation authorizing same-sex marriage, setting up possible Supreme Court showdowns, a majority of those polled - 54 percent - do not believe that gay men and lesbians have a constitutional right to get married. Most support the death penalty, and only about a quarter believe it is cruel and unusual punishment, which would make it unconstitutional.

More than three-quarters believe the Second Amendment gives individual the right to own firearms, but most also think the government has the power to impose restrictions on gun ownership. The rest of those polled are roughly divided almost equally between those who want to see all restrictions on gun ownership lifted - and those who would ban it altogether.

The telephone poll of 1,010 Americans was conducted May 14-17. Most questions have a sampling error of plus or minus 3 percentage points.