As far as I can recall, Matthew, Mark, Luke and John were the writers names - but they were not amongst the apostles. Many people assume they were, and if you ask someone to list the 12 apostles they'll usually start with those names because they are so familiar.
But they are thought to have been close to people who were there at the time of the events. I think Mark for example is thought to be John Mark who travelled with Peter and is mentioned in at least one of the epistles. (Sorry I don't have anything with me at the moment to check that).
The epistles were written earlier, then the gospels at the stage when those who had met Jesus personally were getting old and/or dying, to make sure that the oral tradition was written down clearly to be passed on.
The actual decision on which gospels and epistles to include in the Bible was made later - to begin with the individual ones were used separately, and there were others in circulation apart from the ones we have now. Some were left out of the edit because they didn't add anything extra, others because they had aspects which were considered to be "wrong".
Matthew, Mark and Luke are fairly consistent, though they each include things the others don't, and have slightly different slants on things because of who wrote them and for what audience. John's gospel is more "theological" and takes a different view of things.
As to whether we can say they are accurate - well, that's a tricky one. There's very little evidence outside of the Bible itself to corroborate the stories. Josephus, a Jewish historian, mentions the existence of Jesus as a teacher who had followers, got crucified, and his followers continued to follow him after his death. They were a small Jewish cult at that stage. There's a few other writings which corroborate odd parts, but not anything which would make the central story more "convincing".
I think you have to remember that Christianity is not meant to be a rules-based religion, it was meant (from Jesus teachings) to be about being in a right relationship with God and with other people. The stories which were written down in the New Testament were examples of Jesus' teachings, and some of the history of what happened - the whole Bible is not a set of rules, but the written history of God's relationship first with the people of Israel (Old Testament) then the followers of Christ (New Testament). It's therefore not just a question of picking out a passage and saying "The Bible says you must do x,y,and z" (though people do that a lot!) but if you consider yourself a Christian you should read it and think about what it says overall about how to live your life.