Tradition says you must learn a 12 bar blues first, then all the variations of it, then Autumn Leaves and/or Rhythm changes (a tune like Oleo).
Why do you want to start playing jazz? If it's because you truly like it, then I think you should start by learning the songs you like to listen to. Then follow the progression of tunes above, it's a good and logical method to learn the language of jazz.
If it's because you think you should learn jazz to be a better musician, then listen to lots of jazz to find some songs you like and start with those. "Jazz" is a vast genre and there's probably something in there that can appeal to everyone. If you're coming from a modern pop/R&B/groove perspective, check out the song "Strasbourg/St. Denis" by the Roy Hargrove Quintet, or anything by RH Factor, which is another band led by Roy Hargrove. Joshua Redman's albums "Momentum," "Elastic," and "Freedom In The Groove" are also excellent.
Nobody would ask the question "I want to start playing rock, what are some good songs to start with?" They would learn rock because they like it and they would learn the songs they like. Jazz is just music, there's nothing holier about it than any other style. Enjoy it and learn the music you enjoy before you turn it into a chore and study it.