Part of my character creations concepts regarding to spend CP on skills or not is the character type. Spending CP on skills is relevant for some Classes, especially the more RP focused. I cannot imagine not spending CP on skills for classes like the Student. Those trained dice and specs come in handy more often than not. Classes that tend to be more action oriented, say for instance a "Thug" in my mind, can get by with less skills, as long as characterictic and action cards are available.
Not certain if this works out in practice, but it is something I consider.
More than anything else, like the OP, when creating a character, more than maximizing its power, I think about how I want the character to do things. It really makes the RP experience more enjoyable. Even in combat, because even then, you start to consider the strategy of your character.
I dig it.