The 'guts' of the key of C are 3 chords, C, F and G7. The addition of 3 minor chords, Am, Dm and Em, gives enough of a palette to play simplified versions of many songs.
Take a song from a website. Highlight all versions of the six chords, crossing off any complications like ninths or extra sevenths. Cross out ALL other chords for the time being. Play it with a straight right hand rhythm. You can now play an adequate version of the song. Build upon it, by slowly adding in some of those extra chords.