In the world of scholarly consensus, the earliest fragment of a Greek New Testament gospel is Rylands Library Papyrus P52, containing a few lines of the Gospel of John, and dating anywhere between 125 and 170 AD. As one might expect, there’s a lot of controversy around the exact date. It’s a fragment of a papyrus codex (that is, book as we know it, not scroll, written on both sides); Christianity is believed to have popularised the codex over the scroll as a format.
The earliest complete text of a book of the New Testament is Papyrus 66, a papyrus codex of John, from around 200. The earliest complete New Testament is the Codex Sinaiticus, a parchment codex, dating from the 4th century.