I want to buy the BlackBerry Storm 2. But do I have to have a certain phone plan in order to have one?

Yes, you have to have an extra data plan on top of the regular phone plan!  Right now with Verizon, the Storm 2 is selling for $99.99 with an upgrade or a new 2 year contract! 
specifics:
Stay connected to the people, places and things that matter most with the new BlackBerry® Storm2™ 9550 smartphone. Stay entertained with V CAST Music w/Rhapsody and V CAST Video on Demand. Get more out of life, with tons of great apps available, added Wi-Fi®, next generation SurePress™ touch screen technology and a pre-installed 16GB microSD card for your multimedia files like videos and music. Stay connected, with a solid BlackBerry smartphone messaging experience – on a touch screen – including features like push delivery, instant messaging, Facebook® and MySpace® access, plus email and text communications. And have fun, with the largest BlackBerry smartphone browsing experience, a large, high-resolution screen, 3G technology and video recording capability. It’s powerful, impressive and out of the ordinary – and it’s everything you expect from a BlackBerry smartphone.
All Windows Mobile, Palm, BlackBerry and Android Smartphones require a data feature of $29.99 or higher or a data plan.