It is fun learning songs, but you must learn how to walk into chords, chord embellishments, strum patterns, and the various scales. I signed up for GuitarTricks two weeks ago and have practiced every single day. My playing is so much better because all I was before was an open chord song player. Now I know how to embellish with sus chords, walk into all the major chords (C,G,D) and (A,D,E), Neil teaches this in the "chords and scales" section. My playing is still slow but I am getting better and better everytime I practice. My methodology for learning since I already had some basic chord knowledge, was to complete the entire beginner course with Anders and move on to practicing some of the scales and techniques. I plan to go back and do Lisa's beginner course also to see what I pick up there. I own a Gretcsch electric and a Gibson jumbo acoustic and alternate with country and rock playing to diversify myself.
In summary, I suggest you come up with a plan. If just learning songs is what you care about most, then have at it and have fun. However, I beleive you will really surprise yourself with your own techniques by learning the way I have been doing it. It's fun and rewarding. The most important things though is that you are having fun.