is verizon certified like new iphones? do they work fine.?

Sorry, I don't really understand what you're asking but Verizon is a reputable supplier of iPhones. There's no reason to think they will send you a bad iPhone. Assuming you live in the USA, it will work just fine.

My wife and I each have an iPhone 5 that were purchased from Verizon and run on a Verizon account. We've had no problems with them. Why would you think a carrier like Verizon would want to send out defective phones?

I've received two certifiedl like new replacement phones from Verizon, one iPhone and one HTC Incredible. Both were indistiguishable from new.