[CuddlesBabyCakes]

To win her, guess my favorite CS pet on here. I'll narrow it down some on here.
-It comes in all colors and sizes
-It can be wild and tames
-It has domesticated itself
-There are many superstitions about it
-You can leave it for a week with plenty of food and water and it will be all right
-It can climb up but can't climb down well.

What is it?