In general, the motor needs more voltage to run at higher speeds, because the voltage pushes the current to the necessary level faster. Think of it like this: If you have a /really/ long garden hose, and you want a trickle of water out the far end, you can supply a trickle at the valve and just wait... eventually, the water will trickle out the other end. But if you want that trickle NOW, you turn the water value on full, then wait for the water to start coming out the end before you turn it down. Higher supply voltage allows faster changes to the current and field strenght in the motor coils and so faster rotation. But there is also a balance; at higher PSU voltages the motor will get hotter (because of increased wattage) and it will jerk faster from step to step, so you get more resonance and more problems with stalling. A higher voltage can actually stop the motor getting through resonance bands
Everything in CNC is dynamic; moving loads so what you need to look at is the weight you wish to move or the torque required to move it, and how quickly you wish that motion to be. This is the measure of the power required which can be estimated in Watts and then translated into what amperage and voltage your motors and drive must deliver.
This page: techref.massmind.org/techref/io/steppers.htm#Estimating Has some "rule" of thumb calcs that may help translate the weight and speed you are hoping for into drive wattage, and explains how to translate that into voltage and amperage which will then allow you to pick out a suitable power supply, driver, and motor.
There is also a more accurate estimator that works from the actual measured torque, if you have built the machine.
And finally, there is a calculator that will give you the maximum expected top speed based on the motor characteristics and supply voltage which is, I think, exactly what you are looking for.
If cost is an issue, you might want to look for used motors or scavenge old office equipment for free motors. There is a list with some good sources at: