Everyone's is the right answer because the apostrophe is indicating the possession between the person (everyone) and the thing being possessed (the fact that someone chooses the internet as their favourite news source). It is their favourite news source. Consequently, the apostrophe+ <em>s</em> should be placed after the indefinite pronoun <em>everyone.</em>
Unlike the extravagance of the 2012 Summer Olympics in London, the 1948 London Games were a lean affair hosted by a city still recovering from World War II.
