There are stick welders (that uses 1/8" rod) and there are wire-feed
welders (that use much smaller wire). A 120-volt wire-feed welder using
0.030 wire should do nicely with 1/8" or thinner mild steel. I have
used only flux-cored wire which does not need shielding gas and leaves
a slight powder residue. It's more expensive for the wire, but there's
no need for a flow meter and gas bottle. Both Miller and Lincoln sell
these units which weigh about 60-70 pounds. Mine rides around in a
child's wagon since the unit does not come with wheels.