Hello.
Microstepping can help you achieve smoother motion with stepper motors. I do not see any reason you should not be able to achieve 1RPM without too much trouble. The “Minimal wiring diagram for wiring a 5V microcontroller to an A4983/A4988 stepper motor driver carrier with voltage regulators (full-step mode)” on the A4988 product page shows how you can wire the A4988 to your Arduino. The chart under the “Step (and microstep) size” heading on the same product page shows the settings needed for each micro-stepping mode. You can connect the “LOW” pins to GND and the “HIGH” pins to VDD.
You also might find the sketch in this Arduino forum post and the link to the AccelStepper library for Arduino in this forum post helpful.
-Derrill