So this may sound a little cliche' but the best tunes to learn are the ones that you are most excited about. I used to spend a lot of time attempting to put tunes into categories based on the perception of difficulty. And it is true, some tunes are more difficult than others. Some harmonic concepts take a lot longer to master, and even then are really only mastered when there is a foundation based off of other harmonic concepts. That is also true. So is this: You probably won't learn a tune that you don't like. How badly you want to learn a tune will affect how well you learn it.
There is a body of jazz repertoire that is considered standard. There is a shared body of tunes that musicians work from. Consistently with that shared body is an expectation that this is the body of music that everyone engages with and has familiarity with. Here is a link to a list of 50 Jazz Standards You Need to Know. This is a great list put together by Brent Varista on learnjazzstandards.com. But if you are looking for something a little more surgical than 50 tunes, or a list that is a bit more suitable as a starting point, here are ten tunes are definitely worth knowing. Note, none of these tunes are blues. I have address the importance in other blog posts, let's take a moment and live outside of that to focus on tunes that have a different harmonic fingerprint.
Song for my Father
Bye Bye Blackbird
How High the Moon