For a baking beginner, what cake icing you recommend?
Buttercream is pretty simple, start with room temperature butter, beat it until it's white, slowly add icing sugar, add small amounts of milk as needed to keep the consistency right.  

For each 1/4 cup (1/2 stick) of butter, use about 1 1/2 cups of icing sugar (sifted) and 3 Tbsp of milk.  You can do it in a mixer, a food processor, or just use a bowl and a whisk.  I used a whisk a few days ago when I realized my large stand mixer is overkill for the small amount of icing I wanted and I found that microwaving the icing for about 10 seconds helped me stir in the sugar when it was getting too thick.