[QUESTION] Getting more out of a song!

Once I memorize a song, is there any further study that’s worth while on that song? I do some finger picking, what things should I note after I figure out what notes I’m playing? Rather than just learning what finger on what fret.

I guess, what should I be thinking about while I’m learning it and once I have it learned? I know it’s a vague question, but I appreciate and will learn from whatever your thoughts on the answer is!

Ultimately I’m aiming for some relative play by ear stuff.

Thank you very much!