Because you are already an AT&T customer, you don't need to switch and buy a new plan. All AT&T is going to do is add a $30 iPhone Data Plan, for the Visual Voicemail and Unlimited Internet. All the other features of your account, such as your texting and the amount of minutes you have, will remain the same.
Example:
Before I get the iPhone, I had the Unlimited Texting Family Plan. I could text as many people as I wanted for one flat fee. I had 1500 minutes, and unlimited Nights and Weekends.
When I buy the iPhone, AT&T will add a data plan that allows my phone to access the internet and access visual voicemail without incurring humongous overages. The data plan is an additional $30 to what you pay monthly on your regular AT&T bill.