>>"Will the Link sys act as a booster to the verizon?"
No but the signal strength will be much better due to the close proximity to the end user
>>"Do I use the Verison SSID to connect?"
No. Ideally you want to set up the Linksys to be an access point rather than a gateway. To do so:
-no changes required to the Verizon router
-reset the Linksys WAN connection to default, i.e un-configured
-assign the Linksys LAN side an IP address in the same subnet as the Verizon router. Make sure it does not conflict with the Verizon router's DHCP range, or any statically assigned devices
-disable DHCP on the Linksys
-wireless connections for the Linksys router should be configured in the normal manor for it, not the Verizon
-connect a cable from one of the LAN ports of the Verizon router to one of the LAN (not WAN) ports of the Linksys. If the lights do not light up indicating a connection you may need a cross-over cable (usually only necessary on older units)
-now all devices should have Internet access and be able to easily connect to one another to share resources.
