Hi RM,
Your new MIG welder will work fine for you to start with.
The GTAW process is neater and can make more perfectly sized welds, but it is more difficult to master and expensive to purchase all the necessary equipment.
It will take you a little while to master the mig, but it's very forgiving and the simplest process to work with.
Anyway, once you master the mig, you'll be able to place welds that require little or no grinding to clean up. The best way to learn how to weld neatly is to have to grind your own welds because grinding gets to be a pain in the butt after a while.
A couple of products are available to make cleanup even easier. First there is a gel called nozzle dip which coats the contact tip and nozzle in order to prevent splatter build up. This is important to both extend the life of your tip and nozzle and to keep the shielding gas flowing properly. Second, there is a spray solution called anti-spatter that you spay on the metal your welding in order to prevent the spatter from sticking to you work. Spatter is little drops of weld metal that splash out of the bead while you're welding and make a mess that can be difficult to remove.
A few other things to remember that will help you make good welds are:
Proper stickout, meaning the distance the welding wire sticks out of the nozzle. Keep this distance about 1/2". If it's too short, you'll burn up the contact tip and won't be able to see what you're doing. If it's too long, you'll get a lot of spatter and the shielding gas won't cover properly which will result in a weld full of porosity (bubbles).
Good shedding gas flow, meaning about 30-35 cfh. This helps prevent porosity.
Clean metal, meaning don't try to weld over paint, rust, zinc or other contaminates which prevent the weld from fusing properly with the base metal and cause porosity.
Stay out of the wind, meaning if you're welding outside or have a fan blowing, it will displace the shielding gas and cause porosity. If this is not possible, turn up the shielding gas cfh and make a wind block to protect the welding area.
There are a lot of other things to consider that would take forever to mention here. I suggest that you complete the welding class that you mentioned and study hard. One thing that I know for a fact is that the more you learn about welding, the more you realize that you have to learn.
As far as types of metal are concerned,
For carbon steel, regular old A36 (plate and shapes), A53 grade B (pipe), and A500 grade b (tubing) will work fine, Try to stay away from 4140 or chrome moly as it is specialty metal that requires stress relieving or it will crack. Also, beware of trying to weld cast iron, as it is difficult to weld without cracking. There are a lot of posts about welding cast on this forum that you can find by using the search function.
For stainless, use the grade 304, just because it will work and is cheaper than the other grades. MIG welding stainless with solid wire is a little tricky. It doesn't like to flow very well. Flux Core wire works better. Also, you don't want to work with stainless on a carbon steel worktable and you have to use different grinding wheels and stainless brushes that have never touched carbon steel. Otherwise, your stainless will rust.
For aluminum, I don't recommend that use it unless you get a spool gun and a more powerful welding machine.
Good luck, have fun and welcome to the forum!
Tim