What kind of icing do you use for piping drop lines on cakes?

I'd suggest royal icing as well. If it's too stiff or dry, add some egg white and whip it in.

Do you mean dropped strings? Usually for dropped strings/flowers you would use buttercream thinned with light corn syrup. For more difficult extension work, I use royal icing. It's stiffer, so you can create more rigid designs. But this also makes it more fragile. I also use royal icing for coating and it can be used for over piping, too.

For a beginner, I would practice dropping strings and dots on cardboard before going to the actual cake. Pipe out the design, get it just right two or three times and then move to the real thing.