I will keep it short. The best thing to do until you get extremely savvy with jazz licks and tricks is to stick to chord tones of the chords you are playing over. This sounds very elementary in the beginning but see how successful you are at regular speed simply playing the chord tones over a song like that. Honestly, this song isn't too tricky from first glance. You do have a tonal center (A minor), and nearly all the chords fit into that except C#dim.7, A7b9, and Emi7b5. You also have some altered extensions on the V chord, but it stays in the key center mostly.

There is a ton of books, videos, and tutorials on this subject. Honestly, the best thing you can do is transcribe and listen to the masters and steal their tricks and integrate it into your note. The greatest jazz players worked all the days and nights of their lives to transcribe the licks that made their blood flow and I can tell you that did much more for them than practicing scales. Where as knowing your scales is crucial; listen to the greats and learn from those who made the music, not who intellectualized it.

Kurt Rosenwinkel came to Musician's Institute when i was a student there. Kurt is a fantastic modern day jazz player, and the head of GIT asked Kurt what he was thinking about while he soloed and what scales, etc. he was using. His answer was "Honestly, I have no ideas what I'm playing." As disheartening as that sounds, I think that is the case for most players. It isn't that they have no clue what's going on, but they are simply PLAYING and letting there ears take over.

I can tell you honestly that starting with the chord tones and than transcribing will really, really get you on your way. Know your scales, and I very much value all the knowledge and videos on this site for this subject (Thanks Chris!) But, take those two things into account as well and don't be too caught up in a million different scale choices.

That's the end of my ramble. Good luck. Below is a few videos from some jazz players I love.

Kurt Rosenwinkel
Jeff Parker
Nels Cline