Regarding the rings. They are unlocked immediately at purchase, so for newer players they are best compared to the clan's starting rings.
Wolf- this is really going to depend on how often you end up at 1 hp. Considering the plethora of snipe cards, it's not a scenario you want to engineer for yourself often, but 3 fight is nothing to sneeze at. It could provide the shields needed to save your life; and if you wanted to architect a suicide attack, walking into swamps to activate it could be quite powerful. I'd certainly consider using it before I unlocked Celestite.
Rat- Rats are good at perils and tend to rely on money, so it's a pretty good synergy for someone who avoids direct combat. Evasion is of course better for defense, and the exploding sword better for aggressive play, but definately better than the first 2 rings.
Rabbit- great for rabbit casters, since using tons of money to power trickery only gets you so far. Fills a different niche than the other rings (Sunstone is bad though)
Bear Ring- Like I just said, I dislike Sunstone immensely. This is better because it's easier to activate unless you are trying for Rot (so like quartz, you don't take it if you want rot). Problem is, the best Rot players wont decide to get Rot until after the game has started and they've seen their early draws, quest rewards, and bane spawns. Ergo, I'd like this ring better if there was a way to change what ring you had equipped after the game started.