Post History

The basic answer is simply because those three gospels were in universal use throughout the Church, east west and south. When we consider the actions of ecumenical councils and great synods and things, what they're doing isn't really a matter of "choosing". It's more about identifying the problem, defining what has always been a matter of Church teaching and expressing that to a new (and sometimes misled) generation.

\
So it is with the Bible. Jesus didn't give the Church a bible, or any kind of book. He gave the Church bishops and told them to teach everything he commanded. As the tradition gets written down questions begin to arise over which written documents are to be taken as scriptural. The OT was easy, as they always had the Septuagint.

\
The NT was a little less easy because not only were there edifying but possibly not universally regarded books, there were also floating around a wide variety of Gnostic Christian books and as time went on, the writings of various bishops and popes and doctors and Church fathers as well as various polemics and apologetics. Add to this a variety of both pious and spurious pseudepigraphic works and we can easily see why there was a need to create a canon.

\
As for who actually wrote what and what the sources were and who copied from whom, I'll leave that interesting question to someone interested in the textual sources. I would simply point out that worrying about textual sources and supposed "inconsistencies" rather misses the point of the gospels, as they are simply "memoirs of the Apostles" --- documents that record Jesus's saving ministry, not as a matter of a day by day journal but as works that lead us to salvation written in a universally accessible format.

\
It's my opinion, but I really think the fathers who complied the canon of NT scripture were not really interested in worldly concerns like textual analysis and earliest available sources. They looked at what they had before them and since everyone used these books, that's what got canonised!