Help with CNC machine

Hello
I hope someone can help me.
I have designed a machine which has only one purpose. The machine uses 5 NEMA 17 stepper motors, two pairs of which can if necessary be wired in parallel. As the machine will only have one simple task to perform, I would like to store the .nc or g-code information on an eeprom or SD card.
Optionally; I would like to be able to control and monitor the machine via a small touch-screen, but to simplify the operation for the operator; perhaps labelled push-buttons would be best.
The following functions will be needed:
1. Start and stop facilities.
2. Pause and resume facilities.
3. The ability to set point-zero for all axes.
4. The ability to return all axes to point-zero.
5. A jog facility.
Any advice on which equipment to buy and how to achieve the level of control needed will be greatly appreciated.
I would also welcome any tips on writing a g-code routine or an Arduino sketch which will serve the purpose.
I have looked at items such as: BIGTREETECH Octopus V1.1 Control Board+Drivers For Ender 3 V2 Pro Voron 2.4. Would this or something similar be suitable?

Most decent motion controllers will work this way. Using pushbuttons is all about selecting a controller with enough I/O so that you can send or receive signals to and from what you need to control.
We supply and fit Cncdrive motion controllers on the Routers we build/sell that use UCCNC control software and all of the things you ask for above are easily done. You will just need to choose the controller model which provides the amount of I/O you need.

In terms of how to get the gcode permanently embedded -
What is the CNC machine connected to? Do you already have a breakout board and motion controller? This then needs to be connected to a PC or mini PC then the gcode can be stored on a USB stick and left in the PC to run the code. Same for the mini PCs. There are also standalone controllers which take USB drives containing the code and these don’t need a PC. I only ask the above as you only mention the machine and gcode. There are other bits needed to get it all going so your options depend on what you have now.

You also mention Arduino so I’m wondering if you plan to hook up this to the machine and embed the code there ? Or maybe GRBL ?

Also Nema 17 and Ender 3 comments make me wonder if this is a small machine like a 3D printer, rather than a heavy duty CNC machine?

You will get more specific advice if you can give a few more details on the project and ideally a photo of what you have.