Go to the Verizon store and try them out. There will be 4 operating systems to choose from and many different phone styles: iPhone, Androids, Blackberry and Windows. Androids will generally have larger screens and in some cases you'll be able to do more with them especially when connecting to devices like cameras or external storage (SD cards, hard drives etc.). I think Apple or Windows tends to be a little bit easier for people to pick up and figure out if you are less tech-savvy. Some of the Blackberry's will have a keyboard with real keys. There will be far less app options for Blackberry and Windows. Apple and Android are the two leaders right now.
Determine what apps you might want to use. In some cases there won't be Android, Windows or Blackberry versions of the apps - for example WDWMagic does not have an Android app. Developers are also going to create (and maintain) apps for the devices where they can sell more apps, so for that reason there will be less apps for Windows and Blackberry.
I also think that some of the apps for the iPhones have a better user experience. When I have used an app that exists for both the iPhone and Android devices I've found the apps on the iPhones seem a little more "polished". This is not universally true, but one thing that gives the iPhones and advantage is that there is really only one "form factor" for developers to have to worry about. For the others there are more devices the app has to work on. With all of the form factors to design for, they can't always make an app perfect for every one. For any apps - no matter what platform, check them out and don't buy or install blindly. Read reviews and try to get a sense if an app works or is trustworthy before you use it.
For me, I like iPhone as a smartphone, but Android as a tablet. I can do things with my Android tablet that I can't with my iPad or iPhone. I have friends who are completely the opposite though - they prefer the Android as the phone.
