Concept to keep track of changes in all tables
The answer depends on what you intend to do with the data. Are you going to be doing frequent queries against it or do you only need it for the occasional lookup of what happened when, to rollback bad changes, or for regulatory reasons?

In the first case above, use the second process you descibed although I would add a column to denote the active record. I would also add a record created date. I wouild also create a view of just the active records and use that for allof my code that needs to see the current data. 

In the second case above, I would have audit tables that are populated through triggers (the offective way to create audit records for any change to the db) and that also include the data of the change and the user or application that made the change as well as the old and new values.