I hear that the best "chanell" is sitcoms. Once you watch a news channel, you listen to the professional narrators with a "too good" English. But in everyday conversations native speakers use "another" language, with lots of contractions, idioms, etc.

this is true. I would suggest making sure you understand at least a good amount of the news channel before embarking on TV shows because, yes they, TV shows, will be harder to understand. And movies will be even harder.

Well, 99% of BBC programming will be in British English. And most of CNN programing will be in American English.

Short answer: Any will do. Do you want news or propaganda? If you just want to improve your English, any main stream news source will do. They are, however, written for the education level of 12 year olds. All major news sources are produced so the least intelligent and educated among the population can read and understand them. If you seek a source geared for the more highly educated, perhaps the Economist would be for you. Again, though, there is political motivation in their publication.