K, silly question here but I just want to make sure we've covered all the bases. The black envelope doesn't have a little @ sign in the upper right hand corner right? I only ask because, if I remember right my stock messaging notification looked more like one of those "talking" bubbles you see over someone's head in comics but the stock email app looks like an envelope w/ an @ sign.
Assuming it is the stock messaging notification, go back to the stock messaging app, open the settings dialog and make sure no boxes are checked.
Re: your total message count, in handcent get to the home screen, the one that lists all your conversations, and make sure none are showing unread. If I were you, just to be sure, I'd click the menu button and click "mark all as read".
Now go back to your device's home screen, pull down the notification bar and clear the notifications. The next sms you receive should pop up the handcent notification you choose and if you have selected new message count activated you should see that as well w/ your handcent notification. It's an option, you can turn it off so you only see the icon if you want.
While your in handcent's settings, look around, there are a ton of customizations you can do including different ways to get your new sms notifications.