From http://sqlite.org:

SQLite is a small C library that implements a self-contained, embeddable, zero-configuration SQL database engine.

So SQLite does not have any server component. It stores the complete database in a file.

To use SQLite from Perl, you only need to install DBI and DBD::SQLite. All other modules are fancy stuff that provides mappings from objects to database rows or other fluff that is of little interest to you if you're just starting out with databases and Perl.