I've sometimes suggested to people that if they want to stay informed, just read the news from 6 months ago. It's easier to see what's important and what's just noise when you have a bit of breathing room.
Yeah, you could use the Wayback Machine to check headlines from the past. Though it's not really a practical way to go about things. One thing you could try is to ask yourself if you would be reading an article like this from 6-12 months ago if you came across it today.
For example, would you want to sit down now and read an analysis from September 2016 about who is most likely going to win the U.S. presidential election? No? Then similar pieces (trying to predict elections in 2018, 2020, etc.) are probably not terribly important to you. Would you read a piece from September 2016 about infrastructure issues in the U.S.? Yes? Then that's probably the type of article with more value.
Another would be to wait a few weeks before reading much about breaking news. Some years ago I read the paper daily, and it's interesting how many articles about the major stories are 80-90% the same from day to day with slight updates with the latest information. Better to wait and get the whole story than to get a slow trickle of news with endless rehashes of what you've already been told.
Periodicals that are less interested in breaking news and more interested in long-term stories are good in this regard.
