Ramps 1.4 is one of the proof of concept standards for 3D printer systems. It is a motherboard mostly runs Marlin firmware on it. I advice to to take a look at the firmware if you didn't yet. It is also supporting many motherboards, hardware.
When you open the
configuration.h file in the firmware and search for this definition
#define MOTHERBOARD you will be seeing many options available.
After all, the firmware is the key factor. It contains many engineering solutions in it. So, you shouldn't re-invent the wheel.
All you have to do is to adapt it with some tweaks as per your design specifications.
But, I would worry more about your motherboard (Arduino Uno)
if your design is relatively simple, using less memory and IO pins, it may be just fine. I would consider Mega 2560 instead If I were you.
Good luck with your project.