Learning the "Slang" of a language is not really necessary but as the previous person said, it depends on your goals. If you are aiming to study abroad, the slang won't be something relevant to learn, but if you are looking forward to learn about the culture, you should consider learning the most common ones.

It depends on what your goal is for learning the language. If it's just for conversations or culture, I would recommend it, but if it's for business it isn't necessary. I wouldn't start with it either way, wait until you're comfortable.

In a language institute or at school you would be rather learning the formal language . Although in many literature 'slang' language is used indeed ! If you are learning online your language partner will be many times using 'slang' . Even in business today if you are to meet business men ,it is nice to know the slang of the people or to crack a joke or so. For writing official documents you will not need the slang at all. In short learning the slang will be sometimes be of good use ,specially if you are to live in a native speaking English country and mingle with the people there.

As the others have said: it depends on your aim. Personally, I'd start with the sort of things you get in a good course book: some formal language; a lot of semi-formal stuff; a few phrasal verbs and some idioms; and perhaps one or two slangy terms. It'll give a good range of grammar and vocabulary. If you feel you NEED a LOT of slang... ask yourself why you need it! English is an international language now, and SLANG (and many informal terms/idioms/phrasal verbs) will NOT be understood by many non native speakers. So if you need to COMMUNICATE in business, or in academia, or even in a pub or club, you may not be understood if you use slang. If native speakers use too much slang it is a good idea to ask them to use more formal language - especially if there are non native speakers trying to understand!

Usually learning slang comes after a person has a pretty good grasp of a language. Slang is widely used by native speakers, so I think it's a good idea to know the most common words and phrases...especially if you are planning on spending a lot of time in an English-speaking country or if you like watching movies and TV shows in English. Also, keep in mind that slang varies by country - for example American slang is very different from British slang. I would agree with the commentators above that it's more important to attain a good understanding of formal English first. Learning slang will be the next level.