Your basic idea sounds workable.
A few suggestions and observations:
If you just want to know who was the last person to modify the record, just keep the fields as part of the same table. You won't need a script at all, just fields set to auto-enter any modification data such as date, time, timestamp, account name.
If you want a log of each time the record was modified, use your related table as now you can set your script to create a new record each time. Since most layouts are set up to enable a user to move from record to record, set a script trigger to log the change when the record is committed.
Thanks Phil, starting to get this logic..... ;-)