Hi Hana,
For true Christmas classics song by the musicians that made them "more famous" I love "The Time Life Treasure of Christmas" CD's (2 CD set).
Some of the songs...
White Chrismtas - Bing Crosby
Rockin Around the Christmas Tree - Brenda Lee
Santa Claus is Coming to Town - Perry Como
Adeste Fideles - Pavoritti
The Christmas Song - The Carpenters
O Holy Night - Perry Como
Hark the Herald Angels Sing - Nat King Cole
Holly Jolly Christmas - Burl Ives
Jingle Bell Rock - Bobby Helms
Rudolph the Red Nose Reindeer - Gene Autry
Feliz Navidad - Jose Feliciano
and many, many more... (45 songs total) it is easily my favorite for old Christmas classics.
Another decent with some old classics and some newer is "NOW That's What I call Christmas"
