"The most important thing in learning a language" is a very general question.
It is mostly related to the objectives of each student and the reasons why he/she wants to learn the language.
For a tourist, the most important thing is to learn to communicate at an oral level, without focusing on grammar and syntax, as well as knowing basic elements of Greek culture (what is considered polite, when we use the kinder form of a word/phrase etc.)
For someone interested in studying Greek academically, it is important to study in depth the grammar and syntax as well as the ancient roots of the words. This will give him a much deeper understanding of the language.
For someone who wants to live in Greece and communicate with the locals, it is very important to learn the colloquial language, that is, the language that will be heard on the street, in everyday speech. This is usually slightly different from the official language of the manuals.
For a comprehensive learning of Greek, however, it is recommended that the student use as many sources as possible (books, newspapers, radio and television programs, songs, etc.)