Instead of 7 specific languages, I'd give you 7 categories:

Language categories

A systems language, like C, C++.
A managed language, like Java, C#.
A weakly typed language, like Python, Lua.
A web-server centric language, like PHP, Ruby.
An automation language, like Bash, Batch.
A functional language, like Erlang, Haskell.
A domain-specific language, like SQL, Mathematica.

I was going to make a recommendation very similar to this one, so rather than repeating it I'll just quote for emphasis.  You're spot-on with the idea that other than possibly being directly applicable there can be value in learning new languages in order to expose you to different ways of thinking about how to solve any given problem; you'll get the most bang-for-your-buck in this area by learning different types of languages rather than necessarily any specific languages.  From there it's a relatively trivial exercise to learn the syntax and familiarise yourself with the standard library and idioms of any language you plan to actually use for production.

I would add that it is also a very valuable learning experience to implement an interpreter or compiler.  Bonus points if you at some point design your own language -- even if it's just a "toy" language -- rather than simply implementing an existing one.

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Instead of 7 specific languages, I'd give you 7 categories:

Language categories

A systems language, like C, C++. A managed language, like Java, C#. A weakly typed language, like Python, Lua. A web-server centric language, like PHP, Ruby. An automation language, like Bash, Batch. A functional language, like Erlang, Haskell. A domain-specific language, like SQL, Mathematica.

I was going to make a recommendation very similar to this one, so rather than repeating it I'll just quote for emphasis.  You're spot-on with the idea that other than possibly being directly applicable there can be value in learning new languages in order to expose you to different ways of thinking about how to solve any given problem; you'll get the most bang-for-your-buck in this area by learning different types of languages rather than necessarily any specific languages.  From there it's a relatively trivial exercise to learn the syntax and familiarise yourself with the standard library and idioms of any language you plan to actually use for production.

I would add that it is also a very valuable learning experience to implement an interpreter or compiler.  Bonus points if you at some point design your own language -- even if it's just a "toy" language -- rather than simply implementing an existing one.