The "most popular" is based on the number of channels across all user to which the widget has been added.
The "highest rated" is based on the ratings that users have selected for the widgets.
I'm not surprised that either of those lists don't change that frequently - in particular, a new widget would be at a disadvantage compared to an older widget in the "popularity" listing simply because it hasn't been around long enough to get added to as many channels. However, we've seen some new widgets surpass older ones pretty quickly in some categories. We may want to take a look at some alternative algorithms that might give newer high-quality widgets some better chance to rise above the noise.
As far as "chumby picks" and "featured widgets" - they're chosen by people here and may occasionally reflect certain business relationships, although many, if not most, of them are chosen simply on the basis of coolness. For instance, the Cuckoo Clock and World Wide Weather Guy are unaffiliated third party widgets by regular developers.
The best way to get to be a featured widget is to steer clear of the more "corporate" categories like News, Sports and Entertainment - for instance, I pretty much own the "Weird" category (the three featured widgets are mine), but that's not because of any undue influence by me - I simply take advantage of the otherwise inconvenient fact that I'm weird. If I were aiming to be a featured widget, I'd make widgets in the more wild and woolly categories such as Weird, Clocks, Webcams, etc. - practically all of the featured widgets are done by individual developers.
That's not to say you can't get to be a featured widget in those other categories - it's just that the bar is pretty high at this point.