Assuming you start with a rudimentary vocabulary (know the bare basics), I would say learn listening first, then speaking, then vocabulary, then grammar. Listening will help you understand others when they speak to you, which will be vital for feedback. Speaking will allow you to develop a grasp for the nuances of the language and develop proper pronunciation, with the aforementioned feedback from the conversation partner listening to you. At this point, vocabulary will help you express yourself more clearly and exactly, allowing you a greater range of concrete meanings. Practicing your vocabulary by speaking with new words, further developing your speaking skills, and again, furthering your listening skills. Then grammar would come last because, really, in the English language, they're not so much rigid rules as they are firm suggestions. You can produce a sentence with absolutely horrid grammar, and most of the time, your listening partner will understand what you are trying to say, and offer to show you the proper way to say it in the future.

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My first priority in the English language is listening-comprehension and speaking. In my country people usually spend many years studing English grammar, from primary school to university or other higher degrees, and then, they find out that they are not able to speak or understand English speakers. I think it should change the way a foreign language is taught at schools.