In reference to the compressor I would agree that a 2 stage is preferred but I have painted with a single stage as well, it just goes slower. There are compressors that are designed to run constantly during use providing a constant level of pressure. However, most will want/use at least a 50 gal tank on a normal compressor. You can get away with a single stage if you have a big tank again so long as you paint relatively slowly so that the compressor can keep the tank pumped up. You need to look at what gun you are going to use and what the CFM rating it has, then make sure that any compressor can supply at least that. I run a 2 stage with a 80 gallon tank but I also run a dryer system and a cheap filter on the bottom of the gun.
As to the MIG welder, I have owned and used a lot of them and while a HF unit will get it done, I have found that a brand name like Miller will get it done a lot better. When I did my 70 Challenger I had a HF unit, I welded a fair amount of panels with it (trunk pan, some floor pans, etc.) and it did work (for awhile). Eventually I determined that the regulator wasn't very good and replaced that which helped some, but then I bought a Miller 120 Autoset ad never looked back, that thing (and its 220V brother) are AWESOME!!! they penetrate so much better, deliver really nice welds and generally reduce the amount of grinding you have to do. So, if you can afford it, get a Miller or Lincoln (I prefer the Miller). One side note; the autoset on the Miller allows you to just set the wire size, then all you have to set the material thickness and the machine does the rest, not need to fiddle with wire speed and power.
