Hi James,
Ist Theselonians 5:21 says "Test everything that is said, hold on to what is good". To be up front, I am an atheist. While I don't believe it is possible to prove God does not exist, I see no reason to believe he does. Nonetheless I see many parts of the Bible as writers explaining their philosophy, as was so often the case with the writings of Paul. Or in other ways indicating a quest for truth.
I highlighted your 1 Thess 5:21 quote, since we just read this in our family Bible reading. As a family we read 2 pages of the Bible three or four weekdays per week. Since leaving the faith in 2007 I saw no reason to stop that. Although I have now added reading another book of interest to my children to the mix. Right now we're on the second book of the Harry Potter series. Anyway...
Paul is often wrote out lists. Things that were good, things that were bad, etc. In this case he is concluding his later with a list of good things to do...
Always be rejoicing.
Pray incessantly.
In connection with everything give thanks. For this is the will of God in union with Christ Jesus respecting ? YOU .
Do not put out the fire of the spirit.
Do not treat prophesyings with contempt.
Make sure of all things; hold fast to what is fine.
Abstain from every form of wickedness
I see all that as pretty good advice, although now, I wouldn't use the word "pray" but insead "think-upon" or "self-reflect", etc. You'll notice several folks here provided suggestions about judging what is trustworthy vs not and why. I actually don't feel there are simple answer. I think there are techniques. Reading books from authors you're sure you'll disagree with is a good technique and I agree with you on that. A Christian friend gave me a David Bentley Hart's book Atheist Delusions, that countered Richard Dawkins God Delusion. The Book did not substantially change my views, but I would say it expanded my views on the subject. For example, some atheists are fond of asking Christians, "Why don't you believe in Zues?" Hart's book made my appreciate more deeply the Christian answer, namely that Christianity with its focus on Jesus as the Christ, is a triumph over competing ideas.
Getting back to the Bible, when God pronounced sentence on Adam he said...
In the sweat of your face you will eat bread until you return to the ground, for out of it you were taken. For dust you are and to dust you will return. (Genesis 3:19).
From just these few words we can reach some interesting conclusions, for example that the writer was familiar with the process of baking bread, which relates to farming. But the idea of "dust to dust", which you sometimes hear at funerals is intriguing. I now see modern science taking us beyond what such ancient people could observe. They could see dead bodies decayed and went back to the ground. Coming to the conclusion we come from the ground is a pretty insightful too. Now that we have data from science we can now speak to how right that is. The atoms that make up the 60 trillion cells of our body literally come from material on earth. In fact consevation of energy gives us confidence some of the atoms in our body trace back in time to the very start of the universe. Thus when Carl Sagan talked about us being "star dust" he and writer of Genesis are hitting upon the same idea.
Cheers,
-Randy