lovinspoonful
Smoke Blower
Definitely MIG. I think it is worth pointing out that welding is as much a craft as it is a science. I would definitely get a bunch of scrap and play around with it to get the hang of it and start laying down down some good quality welds. Once you get the hang of basic welding process and techniques, there are all sorts of build techniques that you'll want to learn for working with metal and welding and quite a few that are specific to building BBQ's. Time spent reading through the descriptions of projects here will be rewarded in the design and quality of what you eventually produce. Have fun!