Databases in general and Perl go well together with modules like DBI and DBIx. The nice thing is that those paper over many of the differences between different (SQL accessible) databases by allowing pluggable back ends. There are a large range in the DBD name space.

As for an address book. What is it if not a database?

Take a look in the Tutorials section for Database Programming. Super Search for things such as DBI, DBIx, MySQL, SQLite, DBM::Deep and so on. It's a hot topic around here.