Some of these stories are about women of faith and some have a lot to do with Jewish history.
Books like Jasher, and Enoch should have been kept in. They are quoted from, and referenced to in the bible, and concepts only found in these books are used by everyone from Jesus, Paul, Jude, David, Joshua, there definitely are some books that should have been in the cannon, especially since a lot of the books written were for us in these the last days. Just read through the bible, soaking up as much as you can, and then go through the the books you want. Just make sure to at all times, try them by the scriptures, and if anything contradicts, or deviates, take it with a grain of salt.
I'm reading through Jasher right now, and so far there are some small scribal errors, but for the most part, there's nothing that is huge and contradictory. It only adds to the stories about the events in genesis so far. Gives a lot of insight and understanding to a few events that just didn't make much sense prior to reading them though. Like, how Isaac was cool with getting sacrificed considering he was a full grown man at the time, or why Abraham's brother died in his father's land, what was going on in Sodom and Gomorra that made it so bad, what they did at the tower of babel, how Abraham came to know God, and his relationship to Noah etc, etc, etc. It just gives insight. As Joshua points out, the book of Jasher is a history book, of the deep events that happened.
There's definitely value to be gleamed, so don't ignore them because some people feel absolute hatred towards those that read them, or completely write them off because they feel that because members of the catholic church some odd time ago decided to say they were unscriptural, despite them being used as scripture and being quoted from, and referenced to by several people of great esteem all throughout the bible. If you have an interest, ignore the nay-sayers, pray to God, read your scriptures first, and
then read into the non-canonical books, whilst comparing them to scripture. Not all of the books they removed were legit, because there were several works that came about after Jesus' death and ascension that made their way into the collection of books people would read. But, they got rid of too many books for sure. Just pray, and read and seek it out for yourself, that'd be the best way to go for it.