Have you looked at WWW::Mechanize::Link?

You have the list of links in your array @links. To get at the first link, you can use $links[0].

my $mech = WWW::Mechanize->new();
$mech->get( $url );
my @links = $mech->links();

print sprintf "I have %d links\n", 0+@links;
for my $link (@links) {
    print "One link points to " . $link->url;
    print "\n";
};
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