I agree with Alan Green - carry on with what you're doing, but find some easy songs to play as well. There are a few songs which can be played with only two chords - Horse With No Name, Dance The Night Away (Mavericks) and For What It's Worth (Buffalo Springfield) come to mind. There are literally hundreds, maybe even thousands, that use a I - IV - V progression (A D and E, C F and G, G C and D, D G and A, etc....) and almost as many that feature a I - VIm - IV - V progression - G, Em, C and D; C, Am, F and G.
Once you've learned the open chords you have a huge choice of songs to pick from!
"Sometimes the beauty of music can help us all find strength to deal with all the curves life can throw us." (D. Hodge.)