Hu, this breaks strictures, better use code references :

use strict;
use warnings;

my $state = \&start;
while (my $next = $state->()) {
  $state = $next;
}

sub start {
  ...get input...
  if (/1/) { return \&menu_1 }
  elsif (/2/) { return \&menu_2 }
  ...
}

sub menu_1 {
  ...
}

sub menu_2 {
 ...
}
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By the way instead of chaining multiple if () {} blocks, using a dispatch table is more efficient and looks nicer:

use strict;
use warnings;

my $state = \&start;
while (my $next = $state->()) {
  $state = $next;
}

sub start {
  my %next_action = ( 1 => \&menu_1,
                           2 => \&menu_2,
                           3 => \&menu_3,
                    );

  return $next_action{$_} if exists $next_action{$_}
}
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