Congratulations to passing your A+ test! Keep up the great work and good luck for your next certifications!
will my Cisco appliances be usable with an out connection from the Verizon appliance? I am concerned because the connection that comes into my room from the Verizon router would be considered a LAN connection, not a WAN?
I assume that the connection coming to your room is Ethernet and you want your routers to connect to this connection, right? Cisco routers do not distinguish between WAN and LAN, contrary to some SOHO routers that like to label different Ethernet ports as "LAN" or "WAN". While we also speak about LAN and WAN interfaces when referring to Cisco routers, we distinguish between them because of the interface technology used. LAN interface is today universally understood to be Ethernet, while WAN interfaces are usually (not always) non-Ethernet interfaces, such as serial interfaces, DSL, ISDN, cable etc. However, with respect to passing IP packets, all these interfaces are considered equal.
So as long as your routers have at least two Ethernet interfaces, you can use them to connect to the Ethernet handoff coming to your room (one Ethernet port is for the handoff, the other for your PC).
My computer doesn't have a serial port so will an RJ-45 to USB work (since that is serial as well)?
Yes, it should work. It is commonly used with today's PCs that have no RS-232 COM ports. Make sure it is configured for 9600bps, 8 data bits, no parity, 1 stop bit, no flow control.