If the Verizon device is an Apple device, you can use the native messaging app.
If the Verizon device isn't an Apple device, you might explore various apps (available in the app store), but they all have limitations. Depending on your needs, I'd recommend Talkatone (U.S. and Canada) or WhatsApp (works internationally to more countries.)
To surf the Web from iPad, you'll need some sort of data connection -- wi-fi, my-fi, 3G or tethering to a smart phone. If you set up home wi-fi, it's no additional charge. If you want 3G, you can pay or tether to an existing smart phone data plan (some carriers charge for this). If you go with my-fi, you'll pay. If you use public wi-fi, where you find it, it's free, but comes with security risks.
