Via Stoat, an excellent survey of the epistemological value of peer review by Victor Venema.
In short, if you’re an expert, you already know how much to divide your attentions between peer review and other sources in your field or fields of expertise.
If you’re not an expert, and you’re investigating a field where there is an academic discipline, you would do well to limit yourself to peer reviewed sources .
(I would add: or widely recognized textbooks; often this is the place to start. I would also add that it is best to look for “review” articles to get up to speed.)
Just because something is in the peer reviewed literature does not make it true. Just because something is not in the peer reviewed literature does not make it false. But if you lack a rich intellectual and social context in a field, and you do not have access to someone who does, you would greatly improve your odds by limiting your attentions to what has passed peer review.
(I would add: take the true skeptic’s path. The first thing to do is neither to doubt the publication nor to accept it. The first thing to do is doubt your own understanding of it. You will find that this greatly reduces the number of papers you can read. It is okay to read many more abstracts than papers. That is what they are for. But even with the abstract, question whether your understanding of the claim is actually what the authors are claiming.)