Mine isn't really applicable to either scenario, as I had my iTunes library on my computer. I had also installed iTunes through Bootcamp and set Windows to access the iTunes library on the OS X volume. So yeah, you can store it anywhere.
Where to store it is a different case. It's really a question that we can't answer as it's based almost entirely on your usage. If you permanently have an external hard-drive plugged in, it would be good to store it on an external HDD. There's no point moving it to a different folder on the same computer as it's still taking up the same amount of space and in all events it's just easier to keep it as the default place.
You can move it to a different computer, but again if you want to access it through your main computer you'd have to ensure that the computers are permanently linked or turned on when you need to do that ... again, quite a hassle.
I suppose of the three scenarios you've posed, external HDD would be best.