Both are much easier if you have an RSS feed setup, though I think there's a need for better filtering and self hosted options. You should and can restrict to the main items of a few trusted sources, and the feed need not be addictively designed. You should also set it to pull only one or two items a day from a given source.

A few news sources that have been fine:

Our world in data (covers long term issues like poverty, disease, and climate)

Associated press (fact based and short; most other news is reposting their stuff)

The conversation (accessible articles by academics on their areas of specialty)

And I'll encourage you to find some local news outlet to follow as well. There are some good investigative local outlets, perhaps literally targeted for you, who could both use support and really help you get context.

But with RSS I think you can have a healthy relationship with more classically 'bad' news outlets. If you see who published it before the headline, you can interpret it better.

Finally, I strongly suggest a rule that if you see a headline you must read the article. Block and stop visiting places where you're only looking at the first sentence devoid of context and authorship. If you read an article and it is terribly done, really consider blocking the source. Browser extensions can help.