MIG, the smallest wire you can get flux core that I’ve found is .030”. Its not impossible to weld sheet metal with that but it’s rather difficult.
Have you looked at ready welders? I have no personal experience but it might work for you.
http://readywelder.com/
Another is the Hobart Trek180 if you can find one for sale. It has a battery built in & can be just charged with a small inverter.