Ahh, I missed that part of the OP - sorry. That's happening because the first object in @_ when you invoke a method via an object is the object, not the package name. Thus your $class variable contains the scalar reference and when you print $class you stringify that reference. One way of handling that is to use ref. Something like:

my $self = shift;
my $class = ref($self) || $self;
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If $self contains a blessed reference, ref will return the package name. If it contains a string, ref will return undef and hence the || will return the original string.

I personally prefer perltoot to perlboot. But both are certainly worth working through.