Learning songs is extremely important, if for no other reasons than finances and providing context. You’re not going to get hired for certain types of gigs if you don’t know tunes.
As for the context, in most types of jazz improvisation, we improvise over chord changes of either standard tunes or original songs.
It’s understandable for a young player to think, “There are a bazillion jazz standards to learn. Where do I start.”
First of all, if you learn just one tune a week, that’s 50 in a year.
You can play whole weekend of 4 hour gigs with 50 tunes, or less and never repeat tunes. Also, there are enough tunes that are similar to other tunes, that it will speed up the process quite a bit.
Now understand, when I’m talking learning a tune, I mean melody, changes, and everything… memorized.
Very few things are as bad as going to a gig and having players read every tune, even the most basic blues tune.Also, one of the measuring sticks of a player is how many and what tunes he knows.
First of all, start with a tune that you like. If you are fired up enough to want to learn that tune, you will get it done. That will get you started. Pretty soon, you will start discovering that you need songs of different types, for contrast on gigs, if nothing else.
Some great websites for song lists are: JazzStandards.com (Great historical site), (an extremely comprehensive list by Bert Ligon, a phenomenal pianist/jazz educator from the University of South Carolina) and last, but certainly not least, or all, for that matter, Free Jazz Institute.
Also, in Jamey Aebersold’s various texts that appear with his play-alongs, he has standards catagorized according to styles and difficulty levels which I have used for various student combos I’ve coached. Remember, it’s supposed to be fun and it is a lifetime sport!!!