I use an environment variable per environment (dev, preprod, prod), all telling SSIS where the package configurations are stored.
I elaborated slightly, and have 4 different tables(FTP, Database, File, SMTP). In the case of database, I have my connectionstrings, which SSIS reads and is able to use to connect.
Care to post one of the connectionstrings?
Mine looks like following:
Data Source=YourServerName;Initial Catalog=YourDBName;User ID=YourUserID;password=YourPassword;Provider=SQLNCLI.1;Persist Security Info=True;Auto Translate=False