If it is as you say, and I don't disagree, that the Bible is the thoughts of men (whether inspired or not), then I cannot see how it is any kind of authority. Since the majority of people are unlikely to have the time, commitment and wherewithal to do the type of research that you say would be necessary to reach a definite conclusion, it occurs to me that such folks will naturally rely on the opinions of others who have, or claim to have, done the research already. This is clearly what happens in practice in religions all round the world with obvious results. This seems compounded by the apparent fact that none of the original writings exist and the process of assembling the NT was directed by Constantine and his cronies in the Church.
We are still left with the imprecision I originally referred to: there is no way to be sure that 'God' has played any part in the construction of this collection of documents. Worse than that, if He did, His influence was so weak as to be indistinguishable from human thought. Any appeal to divine authority is thus weakened or, some might say, rendered valueless.
I agree the 'words of Jesus' you refer to were themselves written by men. If the other writings in the books are subject to doubt then so too must it be so with these words. It seems to me there is some doubt that those who committed the words to paper ever heard 'Jesus' speak - if in fact the 'Jesus' as mentioned in the writings existed at all in the form described in the Gospels.
The term 'divine inspiration' is an interesting one. It appears to me to be vague enough to mean almost anything and easy to introduce to make a saying authoritative for the believer without being susceptible to proper analysis. Referring to sayings as 'inspired' without any frame of reference for the degree to which this is true renders them of no more value than anyone else's 'wise sayings' and equally prone to error.
Your final remark is I think quite correct. If a person wants to place "much stock" in the Bible they should research it. Unfortunately as far as I can see, years of study by those with the time and intellect so to do have not resulted in much more than widespread disagreement about the meaning of it. The Church itself has spent centuries in research. I wonder exactly how much more research can be done? if such intense research is required to understand it or determine its validity one wonders why God bothered in the first place as it does not seem a very efficient or accurate way to get His thoughts across. He would appear to have used far more explicit methods in the past: angels, burning bushes, tablets from mountains etc etc.
As a final thought, the original documents (even if they exist any more) were not written in English. I presume that to be sure of what one is researching, one ought to learn Aramaic, Greek and Hebrew too. After all, studying the Bible in English is studying the meaning as ascribed by those who translated it into English, most, if not all of whom would have their own agenda.