A pair of lead acids would be a reasonable place to start. That way you have basically an infinite amount of current available and you will be able to see what the motor really requires, before ordering the PSU if you decide you need it.
I fly RC planes and run cars, yes you will see currents getting on for 60+A maybe on a motor like this, and in cars, spikes of 200A and over are common, but they are just transient spikes. Continuously that's totally unsustainable and I don't think you would need that in a milling spindle anyway so I imagine the sort of PSUs you are looking at will probably work well.