A phone line is all you need. I use two cameras, a Stardot that updates over a satellite modem and an Axis that uses a phone line. That way only a power outage will kill them both.
Axis cameras work pretty good but the Stardot cameras have the best picture.
You can usually pick up a Diamond Supra Express External Modem on ebay for very low money.
The webspace Verizon gives you is all you need. You program the camera with the ftp address, username and password. The camera will overwrite the image every time it sends another image. With a little html programing you can have your webpage automatically update so that a viewer doesn't need to keep hitting the refresh.
If you get more serious you can register your own domain name and set up a webhosting site, that is what I do. It works the same but you can have a custom name and add all the extras you want.
I have a page at this link with more info.
http://www.bearcam1.com/cam_info.htm