Although I like perl's command line switches for one-liners, I question their value inside of scripts (maybe my concept of best practice is wonky). The only one I ever really used was -w but I've given that up for use warnings;. For the example given, I don't see any need for the -a and you can avoid the -n by just coding explicity:

#!/usr/bin/perl

our $type ||= shift or die "no type";

while( <> ) {
  if ( $type eq 'letters' ) {
    print if $_ =~ /[[:alpha:]]/;
  } elsif ( $type eq 'numbers' ) {
    print if $_ =~ /\d/;
  } else {
    print "bad type: $type"
  }
}
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While the -an and the BEGIN blocks highlight TIMTOWTDI, I find the explicit looping makes the script easier/quicker to understand and will be better suited if/when you shift to argument parsing modules.