There is no single way to evaluate a source for reliability or appropriateness. Instead, we must ask many questions of each source. Below are some ways we can look at a source to evaluate it.
"Information resources reflect their creators’ expertise and credibility, and are evaluated based on the information need and the context in which the information will be used." 1 Framework
Whether something is important or can be viewed as an authority depends on the situation you plan to use it in. A tweet about a political policy isn't generally something we would cite. But if the president is the one tweeting it, how does that change the context? A famous speaker might lend authority to a particular management technique, but if they are trying to sell you training materials on that technique from a company they own, does that change our trust in their authority on the topic? If a peer-reviewed article uses an experiment to support its hypothesis, but the experiment was funded by a corporation with a conflicting interest, does that change how reliable we think it might be?
Where the actual newspapers are placed here is of less importance than the two axes. Note that complexity and bias are separate! As for the actual placement, this is just one way of doing it. It's your job to evaluate specifics for yourself.
Sometimes, you can judge how reliable website information is by noting the URL ending.
.GOV - refers to a government website. Highly reliable.
.EDU - often refers to a reliable educational website.
.ORG - implies a non-profit ORGanization. Approach with skepticism.
.COM - stands for "Commerce" and is used for business. Approach with skepticism.