I'm still new at this, but I think I learned the following. At least I hope so.
You are almost right. You need enough amperage to run all 3 or 4 stepper motors at the max amperage simultaneously that they can use. Most likely, this may never happen or only happen for a split second or two. More voltage means more power for the amperage to do it's work. When doing any heavy cutting, the amperage needs to be there to move the stepper/servo motor to its new position.
I realize that this isn't a very detailed account, but it should get the thought across.
Your driver determines what amperage to feed your motor at any given moment. The max amperage to your motor is determined by the Limit resistor size, mounted on the driver, depending on your motor/driver amperage limits. There are formulas on the Zone that will let you determine what resistance and wattage to use for this.
As far as voltage goes, two considerations are taken into account.
1) Motor voltage times 20 (max)
2) Max voltage the driver can handle including any back emf for when the motor stops.
Not all drives are equal in the emf department and should be checked out for what they can handle.
Either way, the lesser of the two criteria is your maximum voltage.
Others, who are more experienced will, I hope, chime in and fix my errors or confirm them. We have some real smart guys on here. Between them almost any correct answer can be gotten.
P.S. The Gecko web site has some very useful information on what you are asking.