I'm thinking about making a Thai red chicken curry with ripe mangoes. Could anyone tell me which curry paste is best for that dish (Choo Chee or Panang or some other paste)?
You want a Thai red curry--Mae Ploy is a great brand.
I have limited knowledge here, but I believe Choo Chee is generally for seafood and Panang is generally for meat. I'd go with the Panang, but if you're buying the red curry paste, read the back of the label. It'll probably give you pointers.
If you're making the paste, try to use a recipe that involves more spices than just coriander, cumin, and red chilis (the basics for Choo Chee). You're looking for additions of lemongrass, ginger, garlic, shrimp paste, etc.
I'm not sure which curries are traditionally combined with chicken, but I second the suggestion of Mae Ploy--their red curry paste is good and not too difficult to find. (And the red is better than their Panang or Massaman pastes, I think.)
Mae Ploy was recommended by the owner of a Thai grocery store, when asked what red curry paste he used in his own cooking. I'm not a connoisseur of curry pastes because they're full of chili peppers, which I cannot eat. But my family reported that the dish I made using the Mae Ploy was excellent. It's the only kind we buy now. ;o)