Here is one I've been meaning to do for years: Autumn Leaves. Written in the 1940s by Frenchman Joseph Kosma, it has become a jazz standard classic that has been covered a zillion times. The chord progression is also a classic and has been used by many, many other composers. I put together an interesting video all about the progression which you can view here.

Not being a jazz player, I avoided the usual be-boppy vibe for this and just concentrated on the beautiful melody/progression and tried to inject a bit of melancholy into it. It is, after all, a song of unrequited love. Most versions are needlessly bouncy and cheerful in my opinion.

I open with a strummed Em6 chord. I'm not sure what prompted me to try that out, but when I did I liked it and so I kept it. Its highest note is the first note of the melody line.

It's interesting and unusual how the repeating four-note melody lines of the verses resolve to beat 1 of the next bar. I can't think of any other tunes that do that. 

My version turned out to be a bit of a jigsaw puzzle of snippets that all (hopefully) fit together into a whole. There's quite a bit of traveling up and done the fretboard and it's fairly challenging. The timing is the trickiest aspect and I recommend -- if you want to reproduce it -- that you work on it one section at a time. I only say that because that's how I went about it.

This lesson is a good example of how to use the right hand, the picking hand, to control the dynamics of the sound. It just happens automatically for me now, I've been doing it for so long, but watch in the video how I mute out unwanted ringing with the side of my thumb. I also use my fingertips for the thinner strings. This is something I developed for playing slide guitar, where it's an essential technique, but now I use it for normal playing too. Comes in very handy!

Have fun with it and adapt it to your own taste and ability. 

(Creating the tab and notation was the most difficult part for me. I never was very good at figuring out timing and time signatures, and this arrangement seems to be a mix of all kinds of feels: straight eighth notes, triplets, dotted crochets. I just kept experimenting in Guitar Pro until I came up with a combination that sounded most like what I played. Use the tab/notation as a reference for the timing and just listen to the rendition in the video to refine it.)