Here is my list of top 20 Jazz Standards(songs) that are a must know as a vocalist and an instrumentalist. I listed the Song title, composer(s) and added a Youtube link. Just know that there are many different versions of each song(including versions with vocals and only instrumental version).
1. Summertime - George Gershwin & DuBose Heyward Ira Gershwin
https://www.youtube.com/watch?v=XivELBdxVRM
2. My Funny Valentine - Richard Rodgers and Lorenz Hart
https://www.youtube.com/watch?v=Fv6Pw7UV4Yo
3. All Blues - Miles Davis
https://www.youtube.com/watch?v=-488UORrfJ0
4. Girl/Boy From Ipanema - João Gilberto and lyrics by Vinicius de Moraes. English lyrics were written later by Norman Gimbel.
https://www.youtube.com/watch?v=c5QfXjsoNe4
5. Fly Me to the Moon - Bart Howard
https://www.youtube.com/watch?v=mQR0bXO_yI8
6. 'Round Midnight - Thelonious Monk
https://www.youtube.com/watch?v=yxwvOncHVbQ
7. Don't Get Around Much Anymore - Duke Ellington
https://www.youtube.com/watch?v=yxwvOncHVbQ
8. In A Sentimental Mood - Duke Ellington
https://www.youtube.com/watch?v=sCQfTNOC5aE
9. Cantaloupe Island - Herbie Hancock
https://www.youtube.com/watch?v=sMxESFBS4mY
10. Take The A-Train - Duke Ellington
https://www.youtube.com/watch?v=Agkj-c-WWGU
11. Do Nothing 'Til You Hear From Me - Duke Ellington
https://www.youtube.com/watch?v=vjApoRdEOi4
12. All of Me - Gerald Marks & Seymour Simons
https://www.youtube.com/watch?v=wFzxo-XI8As
13. Sweet Georgia Brown - Ben Bernie & Maceo Pinkard, with lyrics by Kenneth Casey.
https://www.youtube.com/watch?v=qRbfLlYjsBU
14. How High The Moon - Morgan Lewis & Nancy Hamilton
https://www.youtube.com/watch?v=0w-hkyprwQ0
15. Autumn Leaves - Joseph Kosma with original lyrics by Jacques Prévert in French, and later by Johnny Mercer.
https://www.youtube.com/watch?v=r-Z8KuwI7Gc
16. All The Things You Are - Jerome Kern with lyrics written by Oscar Hammerstein II.
https://www.youtube.com/watch?v=OPapxr8GvGA
17. God Bless the Child - Billie Holiday and Arthur Herzog Jr
https://www.youtube.com/watch?v=bKNtP1zOVHw
18. Lady Sings the Blues - Billie Holiday & Herbie Nichols
https://www.youtube.com/watch?v=KCYCad_Y53U
19. Four - Miles Davis
https://www.youtube.com/watch?v=8xNbqG9PtyE
20. Giant Steps - John Coltrane
https://www.youtube.com/watch?v=30FTr6G53VU
2 Bonuses
1. At Last - Mack Gordon & Harry Warren
https://www.youtube.com/watch?v=S-cbOl96RFM
2. My Favorite Things - Rogers & Hammerstein
