Why are the gospels placed in that order?

Why is it Matthew, Mark, Luke and John?
Wasn’t Mark written first?
Doesn’t Luke have the best Christmas story? Why wouldn’t it be first?
Why were other gospels excluded such as the Gospel of Thomas?

You’re in luck: this has been addressed in an excellent series of staff reports. See Who Wrote the Bible? (part 2, part 3, part 4, part 5) for a complete answer.

Because the early Christians didn’t care all that much about the Christmas story, compared to other aspects of Jesus’ life and teachings. If they had, then all four of the gospels would have the Christmas story, not just Matthew and Luke.

Another thought: John doesn’t fit with the other three, the Synoptic Gospels.

While Matthew, Luke, and Mark tend to share a common viewpoint, they all differ substantially from John. It makes sense for the three to be side by side.

In a word, tradition. In another word, Papias. The first historian of Christianity whose works have survived, Eusebius, quotes an earlier writer, Papias, who claimed that “Matthew first wrote down the logia (teachings, oracles) of Jesus. Mark wrote down the reminiscenses of Peter about Jesus, though not in order.” Luke and John supplemented this later.

This was believed to be the actual sequence until textual criticism came along, and demonstrated that Matthew and Luke are actually expansions of Mark’s narrative by incorporating teachings that were not included in Mark. Since they incorporated those teachings at different points, it is believed that a non-extant source, called Q from the German Quelle meaning “source,” for the teachings, existed and was drawn on independently by the compilers of Matthew and Luke.

It may very well be that Papias was accurate, and that what we call Q was actually Matthew Levi’s collection of Jesus’s teachings. (Matthew was a scribe in the Jewish tradition, earning a living as a tax collector, so would have had the training to compile an authoritative collection of teachings.) Mark is predominantly narrative, with only a sampling of teachings. The editor who produced what we now call the Gospel According to Matthew, and Luke, would have separately drawn on Matthew’s teachings collection, using Mark as a frame story and enlarging on it with teachings from Q/Matthew-teachings-collection. The interesting thing about Matthew is that there are five major “sermons” collecting teachings on a topical basis, where Luke spreads them out more. The preface to Luke (1;1-4) alleges that Luke produced a critical compendium of Jesus’s life and teachings, choosing only the most reliable of traditions regarding Him.

John seems likely to be a combination of reminiscences of John bar Zebedee in his old age with some elaborate theological embroiderings added by editors probably working at Ephesus, where John supposedly located. To what extent it is actual Johannine fact and to what extent theology added on, is a quite debatable subject – Diogenes (who stuidied this in detail) will have some comments on this, I’m sure.