Which is the most important skill for learning a new language? Reading, writing or listening? why?

When learning a new language all skills are equally important. The most important thing is consistency. 

You cannot read a new language without hearing how the word is supposed to sound. In order to commit to memory new vocabulary it is best to absorb phrases in context rather than a list of words in isolation.

As a Teacher and a student, I found stories to be the best vehicle to learning a new language.

Listening and reading will be the initial activities and with time, when the student is more confident, speaking and eventually writing. Time and patience is essential in large quantities.

I'd say that speaking is the most important skill if you want to communicate with foreigners and nothing more. But you won't be able to speak without a decent skill of listening, so they go together. I know a few people who can't write and read, but their speaking skills are pretty good. Of course, you have to learn everything to master a language, so apps like Duolingo are not the best for speaking due to lack of practice. But you can work with a tutor, and I highly recommend you to check Preply because there are native speakers who can teach you, and I think it's great.

Listening and speaking are the most important if you're just planning to travel, but in general, all these skills are necessary if you want to know the language better than a beginner.

In fact, all of the above - language is a complex organism and thus requires a mixed approach

All skills are mandatory for learning a new language in fast and efficient manner

It's very difficult to answer this question, but I think the whole point is that it's worth contacting a professional in your field who will just help you figure it out. I highly recommend you to try the lingopie service through which it is actually very easy to learn a language because you watch your favorite TV series and take it into account!

It’s not easy to say what the most important aspect of language learning is: some would claim listening, some would say reading and writing, and still others would vouch for speaking. The best option for language learning is to not focus on a single aspect, but rather get a well-rounded education that includes all four facets of the language.

But, if you do have to choose, be sure to take into account your goals and in what circumstances you plan on using the language the most.