Songs that have stood the test of time.

There's slight chance to listen to her live while she's still around and actively touring at her 80+. 
Not too much of material placed on streaming or youtube so shop for vinyls and CDs and try to see her live as well.

Hallelujah by Leonard Cohen. Only about 30 years old but has been covered so many times it seems the original (and best) version has been forgotten.

dbtom2 - Tom Landa and the Paperboys have a really good version of All Along the Watchtower.

Check out this My Way cover:
https://www.youtube.com/watch?v=egHWqEDlHuk

"Hallelujah"---great choice! I heard Leonard do it live in concert (if you have a chance to see him live, do not miss it!), but my favorite version remains the one by Rufus Wainwright. Transplendent ;-) !