I assume you have support of your management and required resources (e.g. IT Service Management (ITSM) tool, human resources, etc.). If not - you have to ensure that before you begin.
Since you are small company - don't exaggerate with project (organization) setup. Keep basic characteristics of the project structure.
If you don't know your ITSM state compared to ISO 20000 - do the GAP Analysis (https://advisera.com/20000academy/itil-iso-20000-tools/itil-gap-analysis-tool/).
So, you are ready to start. Following the standard's structure is good idea. You can also see the structure of the ISO 20000 toolkit and follow the sequence of the toolkit (see https://advisera.com/20000academy/iso-20000-documentation-toolkit/)