When you have multiple numbers associated with a contact, and you press call, you get a list of the numbers. The numbers are listed in the order they're displayed in an address book entry: work numbers, then home numbers, then mobile numbers.

Is it possible to change the order of this list and display, say, mobile numbers before home ones but after work ones? (Without actually entering home numbers in the mobile slot and mobile numbers in the home slot, which would just be super confusing.)

No, you can't change that order.

However, when you call the same contact a second and subsequent time, your BB should default to the last called number as the first choice to dial again.