I know you said ideally not using an Arduino, but if you want it simple they're hard to beat as the principle of Arduino's seems to make the electronics and coding as simple as possible. The Arduino Uno has 5V outputs, so you can connect it directly to the stepper driver - no other components required.

The timing diagram Eddy's highlighted would be easy to follow with the Arduino, but for this application we don't need to worry about it too much - just set the step pulse width to at least 5us and it'll be fine.

Just to be clear, do you just want to control one motor at a time? For instance just use a potentiometer to set the speed and the circuit outputs the pulse train to get that speed?

(By all meant do it using one of the other ways suggested in this thread - they all look fine to me.)