I would suggest starting with the Klein and getting through the section on complex numbers, "Playing with C", which is at the end of chapter 1. (Note, Klein has a lengthy chapter 0 which is a review of prerequisites such as functions.)

After that, I suggest moving through them roughly in parallel. You may find that you prefer one or the other; I wouldn't feel bad about running with either one. (In my view, the Klein is more uneven: it has more weak sections, but is occasionally very compelling.)