I am detailing repairs as i go in order to help others who may not have the skills that i do. Where i work, i run a sheetmetal shop, as well as train people up to do aviation sheetmetal for the company i work for. In a lot of ways aviation sheetmetal differs from this. Such as rivets, rivet spacing, aluminum, and stainless steel sheet being used come into play instead of plain carbon steel sheet, a welder, spot welding, then hiding the repair with body filler. However the fabrication of repair pieces is quite similar in both. Replacing floor pans, and quarter skins is similar too.
Preparation is key to a solid long lasting job. If you can solder wire or sweat fit copper pipe, you can wire weld. The key to welding thin sheet steel like this is to NOT get in a hurry. A patch this size will take me about 2 hours to weld in fully. A quarter panel half skin with a non stock seam across the top typically will take me an 8 hour day to fit, ensure panel gaps are correct, and hang in place. It will then typically take 8 hours then to fully seam weld it.
I will space the tack welds about 1 inch apart all the way around then let it cool. All the while checking with a straightege across both pieces that the panels are flat and even with one another. Then place tack welds 1 inch apart centered in between the first tacks all the way around while again checking to maintain flatness between panels and letting the metal cool. Every time you go around the patch you check this. High spots you carefully knock level with the pick side of a body hammer, or use a sharpened screwdriver and a hammer to carefully bump the high spots down.
The keys to not warping the **** out of it are quick tack welds, spacing, not getting it too hot in one spot, letting things cool down. I also use a small 1/4" thick aluminum plate i hold underneath pressed against the seam where i am welding if i can get to it, as well as a copper spoon looking thing with a handle. These 2 items act as heat sinks to help by drawing the heat and help hold the liquid metal in place where its being tacked in. Steel welding wont stick to either of them.
Also cover up any glass and trim with a heavy welders blanket, and leave it covered for the grinding process afterwards, or remove the glass or trim if possible. Orange and red hot sparks from welding and grinding will embed themselves in metal trim and in glass, and ruin it.