AFAIK, Verizon leases the equipment or you can purchase it outright from them. They will spread the purchase price over three months. I don't know if you can use other routers. They supplied one box that connects to the fiber and another, WiFi access point that conne to that.

I recently upgraded my Verizon Fios equipment and plan. The new stuff covers the entire house very well including the doorbell. We pay about $70 a month for 500 Mb. I'm very happy. Their customer service was good too.