I am a huge Mingus fan and early on I thought show tunes and standards wher ecorny and boring, so I learned a bunch of Mingus, Monk and Ellington. Most of them were original forms, or so abstract that they did not have obvious similarities to each other.
I would start with very basic standards, Anything with "rhythm changes" (same form as "I got Rhythm", other basic 32 bar tunes like "Autumn Leaves" and blues forms.
Once you have an understanding of these, you can see what these musicians were working with/against, etc.
I would do a combination of transcription and reading the charts. Also, learn the melodies.
This thread has some great advice:
REALLY Learning a tune