I think the first gospel is now thought to have been Mark, which may have been written as early as AD50-ish. It has the roughest, most immediate style and lacks the narrative embellishment of Mathew and Luke.
I don't neccessrily agree with the that age for Mark, however I can give a better discriptive on why each Gospel has been recorded in the style it was.
Matthew - Matthew is known as the Jewish Gospel, mainly because it written to a Jewish-Christian audience. That is why the Gospel starts with the geneology of Christ and has the tetragre rammaton of DVD which is David with out the vowels as early hebrew has no Vowels and modern Hebrew only has vowel markers. You'll also note that in Matthew's Gospel
the phrase "Kingdom of Heaven" is a fairly common phrase, this is because Jewish tradition thought that saying God's name YHWH(pronounced possibly Yahweh) was inherently sinful because it was seen as taking his name in vain. This and other bits shows that the style the Gospel of Matthew was catered to it's audience so that the could better understand it. Matthew was first recorded for the purpose of being used as a teaching tool, so that while he Apostles where away other preachers would have a reference to use to keep themselves from forming false teachings.
Mark - Mark is the Roman Gospel, it along with Luke are the two gospels that weren't recorded by an Apostle. However John Mark was a disciple of Peter and so this Gospel could be also dubbed the gospel of Peter. Unlike Matthew the Gospel of Mark was not made as a tool to be used to help preachers. The purpose the Gospel was recorded for was to record the sermons that the Apostle Peter gave. That is why this Gospel is shorter then it's companions, it doesn't record the actual life of Christ but instead his teachings. It also reflects Peter's audience, as he was preaching to roman gentiles there would be no point in bringing up jewish traditions as it would make no sense to his audience. In doing thus the Gospel is stripped to it's basics which makes it an excellent first Gospel to read through for new believers as one does not need a background in Jewish history and tradition to fully understand it.
Luke- Luke like Mark is a Gospel not recorded by an Apostle but instead the apprentice of an Apostle. In this case the Apostle is Paul. Unlike any other Gospel, Luke was commisioned to create his Gospel. Also unlike the previous Gospels, it was not directed at a particular audience or recorded recorded sermons of an Apostle. Luke is a Gospel of history, it was recorded for the pirpose to give an accurate account of the life of Chirst and his Apostles. Luke is also a book that is connected directly to another which is unlike the other Gospels. Luke is immediatley followed up with Acts as a continuation of the history of the Church and it's followers(most specifically Peter an Paul). Luke while not as easy to read as Mark is the most comprehensive of the three synoptic(meaning Matt, Mark, Luke) Gospels and is easier to read then Matthew, along with it's follow up in Acts it may be the best book for any first time reader of the Bible.
John - John is the last of the four Gospels to be recorded and was recoded by the oldest and youngest Apostle. John is unlike most of the other Gosples in it's nature. It wasn't recorded with the same intentions of the synoptics, and it's writter was already aware of the existence of Gospels prior to writting his own. John was recorded to combat the enchroaching claims that Christ was only a man. It was also recorded to help fill the gaps left in other Gospels. Becasue of this John is written in a completley different format then the other Gospels, this gospel stresses symbolism and the divinity of Christ. It is often a favorite of NF types to read becuase of it's style but it should be stressed that john needs to be read with the prior Gospels read as that was that was the idea in which Johns audience would have read his Gospel.