CPAN.pm (cpan) is the original client. It comes with Perl, so you already have it. It has the most features. It has a lot of configuration options to customize the way it works, though virtually everyone accepts the default installation. It integrates easily with local::lib.
cpanminus (cpanm) is an attempt to make a zero-configuration client that automatically does the right thing for most users. It's also designed to run well on systems with limited resources (e.g. a VPS). It doesn't come with Perl, but it's easy to install. It integrates easily with local::lib.
Its biggest limitation is its lack of configuration. If you want to do something unusual, it may not support it.
CPANPLUS (cpanp) is an attempt to make a CPAN API that Perl programs can use, instead of an app that you use from the command line. The cpanp shell is more of a proof-of-concept, and I don't know of any real advantages to using it.
In summary, I'd recommend either cpan or cpanm. If you have trouble configuring cpan, try cpanm. If your situation is unusual, try cpan.
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