Don't skip the grammar. We are not kids (I wish we were). The intuitive approach is ok if you want to pick up some phrases or to be able to talk in some standart situation (hotel, airport, etc.). But without grammar you won't make a considerable progress or will make it too slow.
I'd advise to read in Russian as much as possible. As soon as you learn a hundred or two of words begin to read unadapted literature. Try to find some modern popular Russian authors (classics are harder to understand and you'll have to deal with some outdated vocabulary). Reading will increase your vocabulary and grammar skills very fast.