Forgive me but I did look in the FAQ. I want to turn off the beeping when an SMS is received (but keep the visual indicator). How do I do this? I'm totally new to this phone. Thank you for the help.

You need to edit your current Profile. (There's an icon for Profiles on your device.)
Specifically, change the notification settings for SMS.

Wirelessly posted (BlackBerry 8700g: BlackBerry8320/4.2.2 Profile/MIDP-2.0 Configuration/CLDC-1.1 VendorID/100)

You have to edit the profile that is currently enabled. Go to Profiles > Highlight the active profile then press the Trackwheel and select Edit > select SMS > then change the Out of Holster and In Holster settings to None.

Thank you worked like a charm!