You can buy the Jewel Chao in the GameCube version from the Black Market. The more emblems you have, the more jewel Chao are unlocked for sale for rings.
I wouldn't recommend getting one of each stat Chao.

If you want to know what the real rare Chao are, I'll share a secret:
Buy a single-color Chao from the Black Market, like lime green or white or red or whatever. Breed it with a normal Chao. There is a 50% chance that the child Chao will have a custom palette. It will have the same stat-based evolutions and shapes, but the colors (base and accents) will be different.

Each color parent has a different color palette, and the palettes are unrelated to the color of the parent. So try them all out.

At one point, I had a neutral evolution of a custom palette baby Chao for every color egg. That is about as advanced/collecting as I got with Chao, considering how damn long it takes. Though I on and off had a variation of other evolutions as well.