There isnt a lot to a mig, unless its an inverter, so it shouldnt be that hard to put back together, start off with 0.8mm wire and thicker material - about 3mm.
I have an inverter set, but its not as good as my oxford transformer one.
I have used a stick welder as a power supply before, your dicing with magic smoke with one of those, and they are not that suitable for our projects as they usually have a magnetic shunt, when you turn the current down some of the magnetic field from the primary is shunted away from the secondary back to the primary via the shunt (its joined to the big knob on the front), essentially making the trans a current source high impedance supply, not great for electronicians, if you turn the current to max then its resembles more of a voltage source, but if something shorts kapow.