Chronologically, the order of the films is Ringu 0, the original Ringu, and finally Ringu 2, although Ringu 0 was the last movie to be released. The series could be watched in chronological order (with Ringu 0 first) but, if you don't want the mystery of the first two movies spoiled, then watch the prequel last.
I prefer watching it first, but if you want more mystery in the other films, watch them in their release order: Ringu, Ringu 2, then Ringu 0. Note that there is also a Japanese film named Rasen (aka Spiral, 1998) which was meant to be a "Ring 2", but that was later superseded with the 1999 Ringu 2.
The game does pay out, as contestants can win varying amounts of money depending on where their chips land. However, the game is based on chance, so there is no guaranteed payout for any specific contestant. The legitimacy of Plinko and similar games that promise real money payouts is often debated.