What's the model number of your product? Some product has extender mode. If it's just a wireless rotuer, 1. you can configure the tplink as a secondary router. Plug that cable from your Verizon router into the WAN port on the tplink. 2. Tplink working as an access point. Pretty much the same as the first option. Instead of WAN port, plug the cable into the LAN port. And your Verizon router will be the DHCP server in the case.

Model: AC1200
firmware: 2.0.0 Build 20161130 rel.64463 (US)
hardware: Archer C1200 v2.0

If their is a repeater function, I don't know where to find it in the software or how it is labeled. I did your second method listed above but was watching You-tube videos suggesting I need a separate ssid and password anyhow to avoid conflict. I was hoping to have this as an extender using the same ssid and password as the Verizon routers doing the DHCP assignments. Which config is better? I would like everything to be working together rather than having to select a different network ssid for better coverage as I move about the house.

You can set the same SSID and password in access point mode. This is a help guide http://www.tp-link.com/en/faq-1199.html