If you use the wild leg your breaker needs rated at least 208 volts. If you use a two pole breaker, there are straight 240 volt breakers available as some have already mentioned. If you use a single pole breaker - you are not likely to find one rated more then 120 volts unless you are using a panel/breaker system rated for 277/480 or more.
How much power you can draw from that wild leg will depend on the system supplying it. If if is open delta with limited sized transformer for the high leg - you need to watch what you add more closely then if it were a full delta with three equal sized transformer coils, and this applies whether connecting high leg to neutral or high leg to another phase.
If the machine comes with a 6-50 plug, it shouldn't require a neutral for the purpose of supplying 120 volt loads, if it needs a neutral for that purpose they should have installed something like a 10-50 plug.