Your definition of propaganda probably is a little to inclusive. In my experience, the Economist very rarely gets the facts wrong (including by omission of major elements). The "letters to the editor" at the beginning of every issue are also almost always critical of previous issues of the magazine, and they don't have a problem with publishing them.
What the Economist constantly does is give its opinion on the facts, and that opinion usually sums up to how good free-trade and libertarian policies are. I definitely wouldn't count that as propaganda. You could, but then any newspaper with opinion pieces would be propaganda, which is not what is normally meant by "propaganda".
It's certainly not an unbiased publication, it's an opinion paper. From their "about us" page:
> The same page describes the Economist as “a Friday viewspaper, where the readers, with higher than average incomes, better than average minds but with less than average time, can test their opinions against ours. We try to tell the world about the world, to persuade the expert and reach the amateur, with an injection of opinion and argument.”
From the same page:
> "What, besides free trade and free markets, does The Economist believe in? "It is to the Radicals that The Economist still likes to think of itself as belonging. The extreme centre is the paper's historical position." That is as true today as when Crowther said it in 1955. The Economist considers itself the enemy of privilege, pomposity and predictability. It has backed conservatives such as Ronald Reagan and Margaret Thatcher. It has supported the Americans in Vietnam. But it has also endorsed Harold Wilson and Bill Clinton, and espoused a variety of liberal causes: opposing capital punishment from its earliest days, while favouring penal reform and decolonisation, as well as—more recently—gun control and gay marriage."
So you are certainly not going to get "unbiased news reporting". It's a "viewspaper" that takes declared, informed editorial stances. You will get extremely well thought out and researched opinions and analysis.
"Propaganda" is a word usually reserved for intentionally contorting facts to favor a specific political entity. One can have an opinion without spouting propaganda. That's more the MSNBCs, Pravdas, and Fox Newses of the world. If you've ever read an economist article, the difference is obvious.
I honestly think it's impossible to find truly unbiased news sources. That being said, at least most trusted biased sources still root their information in facts and have journalistic integrity. I'm not going to throw out NYT, WP, NPR, Vox, WSJ, National Review, etc. just because they lean in particular directions.
If anything, I'd rather have news sources that are widely known to lean a certain side, because then I know their potential bias beforehand, which I can balance it out by reading articles from opposing publications.
The thing i like about Al Jazeera, is if 20 people die in the west and 50 people die in say Sierra Leone, almost all major media outlets (including international ones) will ignore Sierra Leone and plaster the western incident all over the front page. Al Jazeera at least tries to give some fair coverage to what happened in Sierra Leone and give it a spot on the front page (even if nobody clicks it).