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First you need to determine if Verizon can just give you the modem without the router, then figure the cost of the modem rental. Another option would be to use your own modem and router. Comcast offers that option, not sure if Verizon does.
You can buy a new router if you'd like, but it is an extra expense, and if you aren't experiencing any problems right now, I wouldn't bother.
Probably jaded, I like that sort of stuff. I like being able to find what I am going to use by comparing the electronics to other electronics and comparing prices. I find that fun with anything! Routers, PC parts, etc etc :P