There are issues with Mac's and Verizon's routers. One is speed and the other is connectivity. One thing you can try is take the router off of automatic and set the channel for "9" The other thing i've read is setting the router for wireless "G" only and disable the other options.
Another thing you can try is to set Verizon's router to a bridged connection and use your own router behind the Verizon supplied one.
Regarding speed, I don't know what it is with Apples, but they recognize the issues with FioS and have come up with a fix for Their computers. It's called Broadband Tuner 1.0... Download it and see if it imporves your speeds.
http://support.apple.com/downloads/Broadband_Tuner_1_0