my ($first) = $string =~ /(["()])/;
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<Editor's Note>
From perlop:

If the `/g' option is not used, `m//' in list context returns a list consisting of the subexpressions matched by the parentheses in the pattern, i.e., (`$1', `$2', `$3'...).

Examples:
if ( ($F1, $F2, $Etc) = ($foo =~ /^(\S+)\s+(\S+)\s*(.*)/) )

So, by parenthesizing the character class containing the characters you want to find, the regex will return that character when matched.

The parentheses around the left-hand-side variable (here, $first) are required, to put the expression in list context. In scalar context, a regex will only return true or false.
</Editor's Note>