My parents were fans of Mario Lanza, Perry Como (well mom was), Johnny Mathis, Frank Sinatra, Nat King Cole (and the Trio), Rosemary Clooney, and Bing Crosby among others so I recall listening to the classic vinyls at an early age most of which are still heard during the Christmas holidays softly in the background as we visit with guests and family.
I remember the first time I heard The Little Drummer Boy, Silent Night and Adeste Fedelis (O Come All Ye Faithful) and I really enjoyed them. I still get moved by those songs.
Another one that comes to mind is Do You Hear What I Hear? And my dad singing "Good King Wenceslas" all around the house while he was fetching lights and such.
One of the first songs I learned in grade school which is one of my least favourites, but is quite easy to sing is The Twelve Days of Christmas. I much preferred Away in a Manger and Jingle Bells.
The first songs I remember hearing were White Christmas (the Supremes) and Little Drummer Boy was on a Kid's record so I'm not sure whose version it was. Could have been a children's choir.