In my opinion, the rating should be permanent, without resets, and should include all games for which reports are available on the site. With a time-decaying coefficient. It should also be automatic (not dependent on the free time of a specific person). And before a productive start, all games should be entered into it, at least for a year, to ensure initial representativeness.
I don't see the point in seasonal ratings, as they are more about gaming activity than skill. Therefore, with sufficient desire, many people can easily get to the top in them.