I get the impulse to find the 'perfect' order, especially with a beloved series. It feels like you're optimizing your enjoyment. But with something as consistently well-written as this, there's no wrong answer. The worst that happens is you appreciate a reference later on a re-read.
Start at the beginning. Why complicate it? 'Faceless Killers' is a masterpiece in its own right. It establishes everything you need. If you love it, you have a wonderful journey ahead. If you don't, no reading order trick will magically make you like the rest.