The welding class is a good idea. Most welding shops will give you student discounts. The class will also go over all the safety stuff you should know about. Stuff like phosgene gas, or welding a container that had flammable material in it (un purged) can kill you.
A class will also develop your skills faster, and show you how to inspect and test your welds.
As mentioned, one issue mostly seen in mig welding (compared to other weld processes), is a nice looking weld that has no penetration.
Besides the welder, you will need a helmet, gloves, and a 4" grinder with a wire wheel at minimum. For grinding I like to use 60-grit flap wheels and the thin cutoff wheels. Others like the standard grinding wheels.