Body work is done with a Mig welder. Stick welding is for thicker metal or for serious penetration like when you work on full frames.
Well, you can if you know what you're doing. That's one of the options we had before mig welders became available. You need to use a stitch weld attachment that cuts the weld current in half and small rods. I always had better luck with that than brazing or oxy-acetelene welding. But, yeah, a mig welder is the way to go.
you can buy small migs for a couple hundred dollars that are perfect for doing sheet metal work.. Check the local pawn shops