Papyrus is a ghost, so he actually doesn't wear anything, but he still wears his Battle Armor, Gloves, and scarf. In his 'absolute' form, he looks like a corrupted Gaster in Asriel Dreemurr's clothes.
Before the events of UnderTale, Papyrus was alive and healthy, living with Sans. But when the sixth human came at thee beginning of Snowdin Forest, Papyrus met him instead of Sans. Since the human thought all monsters were evil, he killed Papyrus.
Papyrus still loves making Spaghetti while as a ghost, and still hates puns. Though he does remember all the resets, where Papyrus might have lived.