Is publishing on arXiv early a good idea?
You've left out the option that I think is most common:  post the preprint on arXiv at the same time that the article is submitted to a journal.  Presumably this is the stage when you feel that the paper is ready to be read by a wider audience, and posting it on the arXiv makes that possible without waiting for conclusion of the peer-review process.

And yes, you should update the arXiv version with the "author's accepted version" as long as your publication agreement allows that.