I'm afraid there's no easy answer here. You might get dozens of different answers on how to approach it, but what I think the one thing everyone will agree is absolutely necessary...is to have fun. You could learn chords and scales all day, but if you're not having any fun, you won't stick with it, especially in the beginning. I'm not saying ignore the framework of theory, but at least have a healthy balance.
That being said, I personally suggest you do at least learn the major and minor chord shapes. And sure, songs can be a great way to master these shapes quickly (and have fun at the same time). Listening to music, you should be able to tell approximately how difficult it sounds and if you could try it. Tom Petty for example commonly uses easy chords, yet to great effect.
I took lessons not long after starting myself. My instructor first had me learn the major scale and circled the most used and movable chord shapes in my chord book. However at the end of the lesson every week, he had me bring in a song of my choice to learn. I definitely looked forward to that part of the lesson.