I don't know of any measures of bias, and as you're kind of indicating, you kind of can't trust those either. Anybody more interested in being informed rather than supporting their ideological tribalism is in a really bad spot right now I think. If I'm being honest, I don't think there's a source that's really any good right now. I pointed at Breitbart, specifically because they link things and tend to include large sections of text for quotes. A lot of their other practices are really bad, but aren't at all unique to them. That's how low the bar has gotten though. I used to point to the New York Times, but they've shit the bed so badly recently that they went so far as to publish a half apology and reaffirm their commitment to radical notions like accurate reporting. If they can pull it together, then there's a chance they'll be worthwhile again. A paper I haven't checked in on in a long time that used to have a sterling reputation was the Christian Science Monitor, so I should probably look at that one again. I know it's got a weird name, but when I was a journalist, for that brief flash, it was regarded as being good.
If that wasn't bad enough, there are all kinds of psychological effects that make us inclined to prefer tribalism, confirmation bias and a sense of righteousness.
If I was going to write a general guide, off the cuff, I guess I'd say something like this:
1. Pick a source that opposes the current authority. Power needs to be held to account.
2. Pick a source that values integrity and transparency. This is why I emphasise their willingness to link to sources so much. If an article on say, The Washington Post, talks about the contents of a Trump or Hillary speech, but don't provide a video, or link to a video, that's unacceptable.
3. Wade out into the shit sometimes and see what counter narratives are out there and investigate some of the more interesting ones. Confirmation bias will cause you to reject them most of the time, but at least they'll be there, nibbling at the edges of your certainty.
4. Avoid editorial content as much as possible, particularly on television.
5. Be prepared to switch.
I could probably write a small book about this stuff. It's a tangled mess that hasn't been helped by the failing business models adopted in news agencies, and it's easy to feel informed without actually being informed. Gas lighting was a good choice of term, as it's probably what's happening. If you live in New England and want to have a tin foil hat arts and crafts session, I'm game.