This could get lengthy but it goes something like this.
The inrush current is what happens when you first turn a device on (motor, plasma, lights, etc) and it draws the most amperage. In motors it would be to get things moving, plasma cutters would be to charge capacitors and other electronics. As things get up to speed or become charged the current will reduce to under/at maximum rated input amps. This process happens really fast. In most cases, less then a second. If your circuit doesnt have a time delay the inrush will trip the breaker.
Most breakers and fuses have a “time delay”. This is the time/amperage the breaker/fuse will allow the current to go above the rated amps. Different style breakers/fuses have different ratings.
Deciding what breaker/fuse to use takes a bit of research and know how. This is where a master electrician earns what he charges.
So let’s say your plasma has the specs listed above. As soon as you turn the machine on it would draw 58 amps for a split second. Then it might drop to 5 amps while idle. Cutting at max machine amps is where you would see the 45.2 amps.
You can run an 80 amp circuit but the everything would need to be rated for 80 amps. Breaker in the panel. Wire to the plug. The plug in the wall. The plug on the machine cord. And the machine cord. Unless things need to be debrated based on temperature. But that’s another topic.
The breaker in the panel protects the wire and plug. The breaker in the machine protects the machine.
Same thing goes for a 50 amp circuit.
It will be cheaper running a 50 amp circuit because of the wire cost and material availability.
The 60s and 80s most likely would come with a 6-50P plug, if it does come with a plug. This is a 50 amp plug.
To sum things up. Call an electrician and talk to them about what you want to do. In all likelihood a 50 amp circuit should be good enough.