you should also look at an app called txtforward (from txtForward: Automatically Forward SMS text messages from Android, BlackBerry and Windows Mobile to email), I've been using this app and apps like this for every phone i've ever had. I have filters set up on my GMAIL and it forwards all SMSs I receive to my mail and the filters seperate it. I ahve every SMS I've received for the past 4 or 5 years . Loooove it.
The phone doesn't automatically save every sms or email into a saved folder - you select what you want saved and put it in that folder yourself, using the bb menu button.