Depending on where you are in the world, from a safety regulation point, all e-stops should be of a non-self resetting type i.e. a twist to reset type.
I know in Europe there is also a requirement for all user buttons to work on low voltage (defined as 48V or less), and a reset must be required after any e-stop i.e. the system can't start working again just by resetting the e-stop button.
Now the regs are over, for the size of machine you're using, I'd apply some common sense, as it will be capable of doing plenty damage if things go wrong.
Personally, I'd recommend you use latching E-stop buttons, that control the power supply(s), with Mach being notified of an E-stop having occurred. I would never recommend that you rely on any computer to handle the E-stop, as if the computer happens to be the cause the of the problem, then you run the risk of the E-stop being ignored. By killing the power supplies, even if the computer is doing something it shouldn't, the machine will stop, and remain stopped until you reset the E-stop button.