Which kind of strings should I use for my marionette?

I always used black braided fishing line.  It was strong yet pliable. Depending on where you live though it can be hard to find.  The most common fishing line is the clear plastic fishing line.  The black braided fishing line is used more up north for lake fishing. You might have to find it on the internet. In KCMO I could find it but had to go to a fish and tackle shop. 5 - 10lb should be more then enough.

Would the common, transparent line work as well?

No it it too stiff. Plus it is not really transparent. Light tends to reflect off of it and is more visible then the black. Also harder to tie in a knot. There are some puppeteers that do use it though. I was looking at your puppet you may be able to get away with using a heavy button thread or Hymark to string it.  Looks to be pretty light weight.