Welding is a bit more difficult a skill to pick up. Most guys that do it have gone through about a year's worth of courses and 4 years of apprenticeship. Example, if you hold the rod or wire feed too long in one area, you will create a lump that you will have to grind out... If you set the power settings too high, you'll blow holes through the panel, and if you set too low, you'll not get a decent amount of penetration, so it could fall apart later...
if you're bound and determined to learn to weld, don't start on your car. Find some scrap steel somewhere, and work at it, and learn to weld at different angles once you have learned the basics...
As for a welder, lincoln makes a really good little portable wire feed welder. My friend has one, and he can get proper penetration on 1/4 inch thick steel, and it runs on household ac. If you're buying one, don't cheap out. The cheap models have poor power regulation, and other problems. The last think you want is to be finishing your final weld and have a power flare, causing a blowthrough...
Oh, you'll need a grinder if you intend to weld. Avoid TIG welders until you learn how to weld with a stick welder... The type you want is called a MIG.
http://www.mylincolnelectric.com/Catalog/equipmentdatasheet.aspx?p=59618
You might be able to barter the price down in a shop that's having a slow year....
have fun, and post pics...