My tip is to read a (or more) actual (read: printed) newspapers:
- they are printed daily or weekly (e.g. The Economist), keeping you out of the "Breaking News" loop every 60 minutes; - they have more weight within the news organization because they are the primary driver of revenue; - are therefore written by actual professional journalists in a proper journalistic process.
I recommend just picking up any news paper and comparing that to the online presence of that news paper, you will notice the tremendous difference.
In my opinion, a lot of the "media mistrust" comes from the constant barrage of so-called "news" articles with the primary goal of being shared on social media and bubbling up in Google News. Just check how many news articles are 1:1 copies of AP or any other news conglomerate.