Hi,
you don't mention what sort of software you are running.
If it is a Windows platform then I would guess Mach, UCCNC or similar and if its a Linux platform then LinuxCNC.
I am most familiar with Mach, Mach4 to be precise. Most other systems are very similar but may have particular requirements that I'm not aware of.
I run my machine with a dual core Atom based single board computer with on board graphics and 4G RAM. All-in-all the little PC does not have the power
to 'pull the skin off a rice pudding' and yet it runs Mach4 seamlessly. The only time I notice and miss the power of a bigger CPU and more RAM is when
I load a big Gcode file, say 5Mb or bigger, then the toolpath is slow to load and draw, sometimes a minute or more. Once it loads and draws however
it runs fine thereafter.
The bottom line here is that Mach4 IS NOT a power hungry application, you don't need a powerful or even new PC to run it. If I were you I would save your money
for the best CNC hardware you can afford and steal one of the grandkids cast off computers to run it. You may find that there are specific things that you
want as a result of that experience, then its appropriate to buy new, but something specifically tailored for your needs.
Most CNC software screen sets are fairly detailed and with a lot of buttons and controls crammed onto the screen. They are easier to view with a larger monitor,
but not dramatically so. Mach4 allows you very great flexibility to tailor the screen to your needs, so you could very easily 'de-clutter' the screen and
then it would display on a small screen very nicely.
The only other time where you'd want a big display is if you want to use touch-screen controls. With small screen the control buttons are just too small to put
your finger on reliably WITHOUT triggering the button next door. Frankly when I'm in the workshop my hands are dirty enough NOT to put them anywhere
near the display....you should see how quickly the gunk builds up on my keyboard!
My advice is spend plenty of time researching your chosen software, the motion control board it requires and the CNC hardware you want to control.
Wise choices there will pay BIG dividends, conversely a mistake with any of those will compromise your CNCing no matter how much you spend.
Craig