SQL Server Job logging best practice
Each job step has a setting that allows it's output to be sent to a text file. This can be cumbersome because it's a text file located in the file system and not in a table and might be hard to get to. There is also an option to send the output of a job step to a table. You can query the table, but it's still clunky. (It is hard to write a query to pick the "X rows affected" string out of a blob of text, then pull the number out so that you can aggregate it, etc.) 

I would recommend that you build a simple table in your user database (not in msdb or master) to keep that information. IMO, this is the best way to keep close track of the number of rows affected by each command, particularly if you want to be able to write simple queries to do historical reporting. This way, you can decide to log at the job step level, or if the step calls a stored procedure with multiple commands, you can log a audit record after each command. As always, @@ROWCOUNT is your friend.