There are several types of frostings that can be used to decorate cookies. I have 3 different kinds that I use and I have a definite favorite among the three. You may want to experiment with the following types and learn about the properties of each of them. This will help you to understand why you may want to use one kind over another for specific cookies. I'll explain a little about each of them, and hopefully that will give you a good idea as well.
Meringue Powder Buttercream:
This is my hands-down favorite, and the one I recommend the most. It is a cross between royal icing and regular cake decorating buttercream. It has meringue powder so that it dries well, but it also has shortening in it, so it remains soft on the inside and doesn't dry out the cookie. I like it so well because I think it tastes better than royal icing, and I can get almost as much detail with it. This icing, like royal, can be thinned down with water to make a glaze. Meringue Powder Buttercream takes a little bit longer to dry completely, but once they are dry, the cookies are stackable and can be shipped without damage. The biggest downfall of this icing is that it tends to bleed a little bit more than royal. You need to make sure your glaze is dry before adding the detail work. Even taking that into consideration, it is still my favorite to work with.
Royal icing is probably the most popular icing that cookie decorators use. It is preferable because it holds up very well if the cookies need to be stacked, shipped, stored, etc.. Royal icing can be made into a very nice glaze and also works great for very fine detail work. The biggest problem with royal icing is that it dries hard as a rock, and also tends to dry out the cookies more than a buttercream icing would. The drying rock-hard isn't a big deal if you are doing a cookie that has a thin layer of glaze and some basic outlines or decorations, but if you need a cookie to have thick piping, the thick decorations would almost be impossible to eat in royal icing.
Simple Powdered Sugar Glaze
As the name suggests, this is just a glaze. It is difficult to use for detail work. I like it because it is very simple to make and use, but I rarely use it. The only time I do is if I'm marbling or feathering
, or doing designs that are mostly glazed with very little detail. It doesn't dry out the cookies like royal and it tastes great. This icing can be thickened up with additional powdered sugar to make a basic outline. The only problem I have with it is that the color seems to get a little blotchy and faded after the cookies sit for about a day; however, it's great if you need some quick cookies that will be used fairly soon.