Level of formality, details and updates depend upon many things such as weather, distance from assistance and duration of the voyage.
I have not done trans ocean voyages. I have done off season, implying heavy weather risks, Between Mx Ak running 24x7 as much as possible. For those trips I prepare by:
1 - Using a Garmin inReach.
2 - A set time of day to contact shore side and instructions about what to do if contact is not made more than 2 hrs late. Check the tracking, are we still moving at an expected rate? Are we headed towards our intended next check in point, destination? If so there is no reason for immediate call for help, keep trying to contact us.
3 - A list of who to contact in the event of trouble. People, agencies etc. Take the homework ouf of the shore side person's work load.
4 - Daily check in includes brief comments on boat, crew and wx. Intended postion at next check in or next stop.
I use the inReach for a number of reasons
Near real time tracking data for my shore side contact.
Messages sent include time stamp and GPS coordinates.
Long battery life
Rugged
Easily carried with me in the event of abandon ship along with the EPIRB
Two way comms, not voice but good enough
SOS feature
I use the Explorer rather than the Mini because it has a built in texting keyboard unlike the Mini which requies use of a smart phone app. Smart phones are too fragile and the battery life is too short.