I use MMF (marshmallow fondant). I like it because it is easy, and you don't have to wait for it to dry. I like Rhonda's Ultimate, here in the recipe section. Good luck and welcome to CC. You will soon become an addict like the rest of us 
I love royal icing made with a little almond emulsion to complement my almond sugar cookies
I use RBC (rolled buttercream). Once you have applied it, you can go ahead and decorate it with royal. The RBC is greasy, but if you let your cookie sit out overnight, the greasiness will go away.
Someone else asked this question a while back, and a nice CCer shared this recipe. Unfortunately, I can't remember who it was 
It's what I've used ever since, to rave reviews:
Mix 3 T. of skim milk and 3 T. corn syrup into 3 cups of sifted powdered sugar. Mix completely. Add 15 drops of brite white food color (optional) to help prevent the icing from forming spots when it dries. Divide and color according to your needs. If you want thicker icing, add more 10x sugar. If you want thinner icing, add more corn syrup. Load the thicker icing into decorating bags. Use a #4 tip and outline large areas (#2 for smaller areas). Put thinner icing into squeeze bottles. Flood the outlined areas, easing icing into corners with a toothpick. When the base icing has set -- several hours -- use the thicker frosting and a tip #1 to pipe on details, such as writing. Allow the cookies to sit for 24 hours before bagging or stacking. This icing dries firm to the touch, but stays soft underneath.
Again, thanks to whoever originally shared this recipe!!! Please let us know who you are!
Hi! Welcome to the world of cookies!
there are several threads about types of icing and the pros/cons to each - you might want to try a search in the forum and read through some... they contain a wealth of information from a variety of sources!
Here's on link that might be helpful to you, too.
icing tips/info
http://www.cakecentral.com/cake-decorating-ftopict-588155.html
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