One way to approach this that I would suggest is to go to the site jazzstandards.com and click on "songs". There will be a list of many jazz standards- choose the "rank" option which puts them in a order of general popularity. Click on a tune (like Body and Soul, the first one on the list) and you'll see some suggested recordings and a history of the tune. That should lead you to some recordings- also, most of the tunes listed can be found in jazz fakebooks.
You can also go to iTunes, emusic or Amazon and hear samples of specific singers. Ella, Billie, Carmen McCrae, Sarah Vaughan, Helen Merrill, Dinah Washington, Nancy Wilson, Betty Carter, Blossom Dearie...just a few suggestions to start with. More contemporary singers will have been influenced by many of these.
Have fun!