1. Read Joe Armstrong's Book: Programming Erlang to learn the basics and the philosophy behind Erlang from one of its creators. [1]
2. Read Erlang and OTP in Action to learn more about the OTP (Open Telecom Platform), applications and gen_servers (which btw, you will find them all over).
3. Learn Elixir, perhaps from one of the books Elixir in Action [3] or Programming Elixir. [4]
4. Finally, start implementing your cool personal project.
Ah, one more thing: Elixir School is also a wonderful resource with tons of information and examples [5] and of course the official Elixir website with its excellent docs. [6]
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[1] https://www.amazon.com/Programming-Erlang-Concurrent-Pragmat...
[2] https://www.amazon.com/Erlang-OTP-Action-Martin-Logan/dp/193...
[3] https://www.amazon.com/Elixir-Action-Sa%C5%A1a-Juri-cacute/d...
[4] https://www.amazon.com/Programming-Elixir-1-6-Functional-Con...
http://www.amazon.com/Programming-Erlang-Concurrent-Pragmati...
As such, I'd recommend starting with Erlang rather than Elixir simply because you'll find tutorials on how to start thinking about and breaking down problems to take advantage of the environment; trying to write an Erlang app using a paradigm learned from another language is going to be frustrating and not performant.
Joe released a 2nd edition of Programming Erlang last year, which is a -really- good introduction to the basic ideas of the language, as the focus of it (as compared with the first edition) is very much beginners, and taking advantage of the platform. http://www.amazon.com/Programming-Erlang-Concurrent-Pragmati...
When people hear "functional programming" many of them will immediately point you to Haskell (and totally forget to mention The Haskell Pyramid [1]). I'd advise you to stay away from it until you _want_ to go deeper down the rabbit hole.
Play with Elm and Erlang ("Programming Erlang" [2] and "Erlang Programming" [3] books are great) to un-learn imperative patterns, tinker with OCaml to learn a new way to modularize code.
[1] https://patrickmn.com/software/the-haskell-pyramid/
[2] https://www.amazon.com/dp/193778553X
[3] https://www.amazon.com/dp/0596518188