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

I'd be tempted to do a 40 amp, maybe 45 amp double pole breaker. Granted the welding outlet is rated at 50 amp, nothing says that you can't down size the feed to it; wire size is very important, especially the further away from the breaker your out let is. Breakered at 50 amp, you could be pulling up to 4AWG size wire if your breaker panel is any distance from where you have your out let, at a minimum I'd use 8AWG size wire at 40 amp.

Remember the breaker is protecting the wire of the circuit and therefore your house, not the welder.