The iPhone 3G is really outdated. Yes it will still run apps, but many apps are only available on newer models (iPhone 4 and newer). Also those phones are the only ones that can get the updates, like iOS 6 and soon to come iOS 7.
Apps that require a front-facing camera will not be available on an iPhone older than the iPhone 4. However you can use it for Internet just fine and the apps that come with the iPhone. Facebook, Twitter, Instagram and other social network apps should work fine. You can check for app compatibility in the App Store.