If you're going to be using concrete to surround your post, then 12 inches (300mm roughly) is an ideal width.
Post hole digging is easiest when using an Auger Drive (Post Hole Borer) powered by an earthmoving / agricultural machine - these include skid steer loaders, mini loaders, tractor loaders, telehandlers and excavators.
Depending on the type of ground you're drilling into, you will need to select the correct auger to suit your application:
Rock Augers: Recommended for drilling through solid ground (not recommended for clay)
Tungsten Augers: Recommended for drilling through clay and rocky ground
Earth Augers are also available but are far more limited in their suitability to different ground types.
The size and hydraulic oil flow of the machine will determine the model of Auger Drive you require.