Nothing is set in stone, but here are a few very general rules of thumb. Blue shadows look GREAT with brown eyes, but brown eyes are really diverse in that most colors look good with them. If you have blue eyes, it’s important that you choose a color that is darker than your eye color, (otherwise you can look very washed-out) and try going for silvers and warm colors. Green eyes look great with those reds and plum colors, but try not to use too much red if you have pale skin, as you can make yourself look sickly.
The answer to this is: it depends. I would suggest starting with eyeshadows/pigments, but the color of these totally depends. Depends on..? On you. On your skin tone, on the color of your eyes, the color of your hair/brows, and on your tastes. As a totally basic color, it would be nice to purchase a light (shimmery or matte according to your taste) color that can be used as a highlight (I use Shroom — I also like Phloof! and Blanc Type). This is a color you will use every time you do your eyes, so it will go quicker than other shadows. You’ll also discover that at times when you don’t feel like being so dramatic, you can put this color all over your lid and have a very simple look. Because building your makeup collection is so dependent on your own tastes and your own face, your best bet is to go into a MAC counter and play around with the different products. There are several different eyeshadow finishes and you’ll develop preferences over time. I find that the swatches on the website are a lot less accurate than they could be so I am always weary of ordering without swatching myself.