If you had previous types of connections like dial-up or ISDN and don't intend to return to those setups, I highly recommend deleting all such old preference settings from your system so that they don't cause you or your Mac confusion in terms of what settings to use in System Preferences networking or local preferences... It's just good house-keeping and problem-prevention if you know how to properly clean out those old use-less settings. If you can't locate them or delete them in system preferences, you can find them as a .plist file in user/library/preferences and sometimes in the by-host sub folder off that. You will have to have an idea what they are called or you can really mess things up by deleting the wrong preferences files.
Is this current connection you're speaking of a DSL connection or FiOS?
If you have a FiOS connection, you can ignore almost everything Verizon tells you about proper setup on a Mac or a PC. I have Verizon FiOS and have completely done-away with their slow 802.11g-only WiFi router in terms of my computers' access to the Internet, but I still have to leave their router connected only for the TV onscreen guides, apparently. Verizon tech support will always tell that you have to use their wireless routers first in-line with their ONT fiber connection device or you won't be able to connect to their network and they can't help you with troubleshooting. I found out by ignoring their directions and connecting the devices in the order I thought they should be connected for my best speed, I had no problems in doing so. I connected them in the order FiOS ONT (10/100 Ethernet)--->to AirPort 802.11n (with Gigabit Ethernet)--->to Macs with 802.11g or 802.11n WiFi, two 10/100 Ethernet wired Macs, and a wired 10-megabit non-router network hub (using NAT settings in AirPort) for connecting the slower Verizon-wireless router, networked HP printer, and some PCs on the same level below my AirPort router. To do so just requires resetting (or power-cycling) all the network devices (including the ONT) so that they all recognize the MAC addresses of what's currently connected. I've never needed to use Verizon's silly add-on software. That's only going to make things unnecessarily more complicated and slow for an intermediate or expert-level user. Novices who can't trouble-shoot their way out of a box might want to consider using it the way Verizon tells them to though.. 😉 If you are using a DSL connection, then ignore what I just told you. DSL may require use of PPPoE or some other weird connection setup which IF the Mac System Preferences networking settings can't configure by itself will require the use of Verizon's bloat-ware, unfortunately.