I run my Miller Mig unit on a generator all the time. the Genny is on my trailer, and I wired in a plug inside the trailer for the welder. It had the 4 prong "round" connector on the genny, Using a plug from Home Depot that fit the genny, wired in a 10 ga 25 foot extion cord form Haber fright, into a socket that the wilder would plug into( from HD). total cost was less than $30.00.
I was not sure of what terminals to connect to, so used a Volt Ohm meter to find the 220 V terminals and the ground. running the genny to determin them. Connected the white and black wires to the 220v and green to the ground. Connected the other end to the socket the same was and it works great.
I would post some pic's of it in the morning if I knew how to add pics, which is something I need to learn how to do anyway as

Most posts are,....
The 20a Genny will work fine, may not support the full 225 amp settings, but most times that much heat is not needed. would certainly pull 150 to 175 welding amps.
It sure is nice to have spell checking on here.....