Not all jazz tunes are created equal. Some of them are constructed in such a way that they help us learn other tunes (or play other tunes better).
Here are a few jazz standards that pose particular challenges that will make everything you learn after them a little easier:
"Cherokee" If you're used to playing in Bb and F, the bridge to this tune will give you a good challenge as it moves into the keys of of B, A, and G. In particular, it gives you a good workout with the ii/V/I chord progression in these keys, which you can then apply to other songs. At first you'll struggle, but eventually you'll get comfortable in those tonalities and find that your "usual" keys seem so much easier all of a sudden!
"All The Things You Are" Sometimes abbreviated as ATTYA, this Jerome Kern classic continually shifts the tonality in a way that other common tunes, like "Autumn Leaves," don't. It will take a while for the chord progression to feel natural, but once it does you'll find that other tunes seem simple in comparison.
"Confirmation" This complex bebop melody will give your fingers a workout, especially during the bridge! My jazz piano teacher Billy Taylor recommended using the melody of "Confirmation" as a model for bebop soloing.
"Giant Steps" Countless jazz pianists have struggled to remember where they were in this circular tune that doesn't follow a traditional form. There's something about it that will get you thinking in a new, exciting way.
"So What" With only 2 chords, "So What" is so easy to improvise over that we don't often think of it as a tune that will help us with playing more complex chord progressions. But by soloing in the tune's modal style, you'll free up your melodic concept which you can then bring back to more complex chord progressions. Your overall soloing will get better without your even knowing it.
So there you go: 5 famous jazz standards that will help you learn other tunes better. Practice each one for a month and see what a more fluent player you've become in less than half a year. Good luck and have fun!
If you're looking to take your jazz playing to a new level, check out my jazz piano video course. I'll also give you personal guidance and instruction along the way!