And the more asterisks, the better. I think three is the top (for now) that a skill can have. Below is my current stats with Lin, on day 289.
For right now, I believe the three asterisks maxes out a skill. There's three colors before you get to the yellow I believe; green, blue, and purple. I don't remember though the order of them when it comes to improving a "skill."
Somebody else may be able to enlighten us but even with the 26 runs I've done of this game from beginning to end, the colors were not something I paid much attention to on this screen