The honest truth is that you get the greatest experience and skills by playing with others. You will learn how to suite different musical situations and learn to listen to other people play. Simply learning songs is beneficial, but after you get a few of those things under your belt go out and meet some other players at your level or above. Also, perhaps take your skills and teach them to someone else whom wants to learn as well.
Working with a metronome is another great way to hone your rhythm chops. I am assuming you may already have worked with one playing scales, but change your routine to playing different chords with new rhythms. Have your teacher give you some chord progressions and different rhythms from songs that you enjoy.
These are just a few tips. Again, nothing replaces playing with others. Feel free to post any more questions.
Douglas Showalter