'Suitably simple' means

1. No use of the DATA filehandle.
2. No verbosity over STDERR.
3. No reliance on perl run options in the shebang line.
4. Runs under strict and warnings.

If you notice other restrictions, please let me know. I'll add them to the list with credits.

Here's the code:

#!/usr/bin/perl -w
use strict;
{
    my @lines = map { chomp; $_ } <DATA>;
    # magical input permits interactive, piped, or
    # batch operation.
    push @lines, map { chomp; $_ } <>;
    {
        local $, = $/;
        print @lines,'__DATA__', reverse @lines;
    }
}
__DATA__
#!/usr/bin/perl -w
use strict;
{
# This block prints the source to this program on stderr.
# It quines there so that scripts which write to stdout
# can operate unimpeded. Generated by quinify.
    my @ary= map { chomp; $_ } <DATA>;
    {
        local $,=$/;
        print STDERR reverse( @ary ), '__DATA__', @ary;
    }
}
[download]

I use reverse to mung the source in data, mostly for visual effect. Any encryption-decryption scheme may be used, or none at all.

This may look familiar. I used a previous version, with a mildly obfuscated __DATA__ section, to quine There can be only one! in But There Are Two! .

After Compline,
Zaxo