Unfortunately, Verizon's wireless router is downright awful - and if it's like mine, it will default to WEP encryption. WEP encryption is weak at best, difficult to configure and can be broken in a matter of minutes, with readily available tools.
My recommendation would be to disable the wireless radio on the Verizon modem/router combo and get a real wireless router.
Barring that, you may want to give them a call and ask them to walk you through configuring the router for WPA security. You'll then have to reconnect your wireless devices/computers, but the benefit in terms of speed, security and overall reliability will be well-worth the effort.