I've noticed that many people have an impression of jazz as being very technical and abstruse. Personally I got into it as a young teenager just because I liked the way it sounded. I didn't know anything about its cultural context and certainly nothing about musical theory (in the meantime I've learned a bit about the history of the genre, but still remain completely ignorant of musical theory).
My approach with jazz, as with any other piece of art, is to enjoy in the simplest and most direct way the things that give me a nice feeling or that challenge and surprise me and at the same time to discard those things that I don't like. I suspect any professional or serious aficionado would find this approach childish and rudimentary, but I don't care in the least.
> a series that could teach you how to listen
If there is such a thing I think you should run away from it. At least as a consumer of art you should look into the things that speak to you personally without regard for how high-brow (or low-brow) they may be considered. This is not to say that you should immediately dismiss things that are 'too fancy', but just that it's OK not to like them.
I get where you're coming from, I didn't get into jazz until I started playing myself. You can certainly appreciate it more when you understand what goes into it and why. Same goes for so many things in life.
That said Miles' album Kind of Blue which has been mentioned here I think is an album that can be appreciated by anyone and for me personally served as a gateway to more complicated jazz. There aren't any fast-moving complex harmonies, the framework of the songs are simple. Coltrane's and Cannonball's solos are fast on some songs, but not that complex or weird to a non-trained ear (I'd assume) and they are also very melodic (especially Cannonball's).
I think there are a couple of things that make jazz tend towards being more "difficult" for lack of a better word. One is that for whatever reason, jazz accommodates music with a very high level of complexity, and it's fun to go there and explore.
Another is that jazz no longer rules popular music, and is therefore not constrained to produce music that is "utilitarian" in the sense of being able to sell lots of records, fill dance halls, promote consumer products, etc.
It is a good watch but that's what peeves jazz nerds.