Just did this transition and there are some things that are a little tricky, here's a list:

1. There isn't an easy way to migrate mail. Assuming you aren't a big company, the easiest way is to just have individual people open up mail in their Outlook or Mac Mail clients and copy the mail back and forth.
2. When you copy documents over from OneDrive to Google Drive, if you want to really edit them well, you should convert the running documents to Gdocs format or at a minimum DOCX. Then you can do online collaboration.
3. Create some Shared Drives with different departments. This is a good way to manage security in a small company.
4. When you want to work on a document, make sure to share it to others, by default people won't be able to see documents and this is a way to make sure this happens. You can turn link sharing on as well, but beware of the security hole if you also allow people outside your organization to access documents.
5. You don't need to be obsessive about versions and copying all the time. GSuite keeps track of the entire history of the document.
6. The one case where you want to export is if you are ever going to close the organization. Gsuite has this notion of owner and if the owner goes away, the document seems to. This might be a bug, but beware. Hard experience here!

The nice thing is that once this is all working in a typical startup, you can just post a standard sales agreement and it is always live and there.