MIG or TIG as already mentioned. TIG is better because you can keep the heat down to almost nothing. You can litterally weld a beer/soda can back together with a TIG, it is the only kind of welding you can do this with. Body work is definitely not the place to start learning to weld. However, for body work you do not need a big machine, a 110v MIG will do the job fine. For MIG always weld with gas, flux core wire is not good and only for using outside where wind will blow away your shielding gas.
Take it to a body shop because you also need painting and color matching. Most body shops do not deal with the inside correctly though and leave the metal/welds raw which leads to rusting again. So you will want to check inside the panel after they are done or speak with them specifically about this before work is performed. You can POR15 or Rust Bullet inside the panel after they are done and that will take care of it for a long time.
Here is something that is a bit of a myth for people who do not know body work. Body filler is not a bad thing at all if used correctly. Almost every body shop uses it, including high end restoration shops. Some car manufactures even use it as vehicles come off the assembly lines, for reals, no joke. It is NOT meant to fill holes or be thicker than say 1/16-1/8". It is NOT meant to be put over rust. It is meant to smooth out panels and deal with minor imperfections. I have done $100k restorations where we had over $25k just in the body resto and paint so am real familiar with all this and learned a lot on those projects from guys that are true pros.
Cheers
