First document to have as a starting point for lab quality system

If I may to reply to your second question first

You asked

do I have the option to implement the LMS manually or can I buy or get the software to implement it because it looks like too much work

You can use the Advisera ISO 17025 toolkit to implement ISO 17025 yourself. The general, management, resource and process requirements of ISO 17025 can be implemented via the provided templates for procedures and records. Guidance and support is also available via other complementary resources. Understandably, the technical processes of your operation must be known to you. You will use the templates and records to ensure the mandatory processes are documented and objective evidence recorded.

You also asked

what is the first document to have as a starting point

This is a good question, as planning is crucial. The toolkit documents are provided in the sequence you are recommended to follow. The first toolkit project document is the project plan (not mandatory) to guide you. After determining the scope, management commitment and responsibilities you will first write your Quality Policies, Quality Objectives and start on your overarching Quality Manual. Once you have looked at the risks and opportunities within your processes and system, you will continue defining the processes and document the other procedures.

Have a look at the preview of the ISO 17025 toolkit at https://advisera.com/17025academy/iso-17025-documentation-toolkit/

You can download the free Diagram of ISO 17025:2017 Implementation Process, the Project Plan as well as relevant white papers at https://advisera.com/17025academy/free-downloads/