It could be weekly or monthly, with a mix of new games and classic gems that maybe aren't so well known. I'd tolerate a fair amount of advertising or sponsored content in the newsletter as long as it was clearly labeled.
The key thing for me is quality. I think that's true for many (extremely) casual phone gamers. I'd much rather get 1 outstanding recommendation per week/month than 10 of varying quality. And I know game enjoyment can be somewhat subjective, but there are still some games that are generally well-done and broadly appealing to fans of a genre. If the top recommendation is a racing game, I might skip it. That's okay. I don't need a new game every week or even every month. I just don't want to waste my time sifting through bad games or games that start fun but quickly ramp up the IAP pressure.
HumbleBundle kind of fits this niche, but I found their volume to be too high. And frankly, I don't want to buy a bunch of games at once. I think I'm less of a gamer than their target audience.