What is the minimum size breaker for this welder???????

How is the wire being run? Conduit or Romex? I believe that #8 thhn can be on a 50A breaker, where as #8 Romex is limited to 40A. Got an electric dryer? If you're only going to use it a few times might plug it in there.

Electrician here.

Dryer might work depending on heat settings. Most dryer plugs are only 30a though.