ISO 20000 implementation order

Answer
ISO 20000 does not require any particular order in which requirements will be implemented. But, from the experience point of view, I would recommend to:
1. establish the SMS (Service Management System
2. Implement the processes

There are two elements which can help. First one is to follow the order in the toolkit (you can see the list of documents here https://advisera.com/20000academy/iso-20000-documentation-toolkit/# .
Additional help could be "ISO 20000 implementation diagram" https://advisera.com/20000academy/free-downloads/

On the other side, ITIL needs different approach, and you can get useful ideas in the article "Ready, steady… go – Starting ITIL implementation" https://advisera.com/20000academy/blog/2014/06/10/ready-steady-go-starting-itil-implementation/