Does your rhythm still have no authority? I could play lots of chords and my rhythm was still poorly developed. Your sense of rhythm will continue to lie fallow unless you have studied rhythmic strumming while counting time out loud. To play a whole song through is the goal and to do that you must have developed some concept of time, measures, beats and developed some stamina.
I recommend you practice rhythm as soon as you have learned your Diatonic C scale and chord scale in the key of C. The I-IV-V is C F G.
Many Beatles songs use simple basic chord movement. Pop Songs are usually simple. Lennon McCartney were master songwriters and as totally original as possible even coming from a derivative school of American music and skiffle music. They must have had some basic formal musical training and are respected master song writers studied to this day. George Harrison was no slouch either. Try playing 'Something'. Brilliant song or his 'My Guitar Gently Weeps'
This Beatles guitar lesson has some easy simple guitar music but the tunings could put you off. It also has more challenging songs. Its a mix of difficulty levels. Another good sorta-kinda simple guitar lesson with pretty much these exact same tunings is the 6 string Nirvana lesson with Doug Boduch. That way you could learn a Beatles Lennon-McCartney song and then a Cobain-Nirvana song in the same tuning without the hassle of re-tuning. Its just a thought or buy several guitars, one for each tuning. You know you want to! A Chromatic tuner is your friend.
Acoustic Lennon & McCartney Page One | Page Two | Page Three | Page Four
Two roads diverged in a wood, and I—I took the one less traveled by, And that has made all the difference. –Robert Frost