You refer to "jojo kanji", but I assume you mean "Joyo kanji", of which there are now 2,136 (previously 1,945). By and large these are the most common kanji, and most learners concentrate on them to start with. To say that they are "not common in Japan" is ludicrous. There are other kanji outside this list that you will encounter from time to time, but if you know the Joyo kanji (as well as knowing the language itself, of course!) then you will be able to read most ordinary modern Japanese texts fairly satisfactorily (I do not know specifically about games and songs). Proper names (names of people and places) are a slight exception because non-Joyo kanji are more frequent in those. In fact, there is another list, called Jinmeiyo kanji, which contains a whopping 861 more characters "officially sanctioned" for use solely in names.
Because it takes a long time to learn 2,136 kanji, it obviously makes sense to learn the most common ones first. This should happen automatically if you follow any sort of sensibly structured learning programme. As Mike says, it is daft to try to learn kanji in isolation from learning the language itself.
In my opinion it is possible learn to read Japanese by yourself, with the help of textbooks, websites etc., and maybe with some help from people at forums like this. Expect it to be hard work and to take years. However, I do not believe that it is possible to become competent in conversational Japanese without having a huge amount of practice with other speakers, preferably native speakers.