Here's what I have come up with for my lighting choices.

[Village Idiot]

How would I know when to use 45"?

The bigger the light source (and the closer to the subject) the softer the light. So if your goal is nice soft light, then a larger umbrella can give you that. Some would even say that larger is always better...up to the point where it's just too big to be practical.

But you have to consider that if you are using a hot-shoe type flash, a larger umbrella may not make much of a difference.

This. The hotshoe flashes generally have a built in reflector with a limit on how wide they can go, so no matter how large the umbrella is, the flash can only cover so much of it until you find a way to mount the flash farther away from the umbrella and at that point, you're just being silly.