A cheap gigabit router from Walmart, OfficeMax, or Best Buy and hook up The NVR and trunklines to it (provided you have enough ports) will suffice. You also could make everything static and reuse one of those free Cisco switches. Assign static IPs to EVERYTHING. Make sure everything is on the same subnet (e.g. 192.168.1.0/24 is a common one), add all of your cameras manually to the NVR and that also will work. Internet is only required for remote access. Standalone, what you have will most definitely work without buying anything, just need some config changes to make everything work (you'd need to do that anyways).
NVR --> LAN NIC (abandon the PoE ports) --> Cisco switch --> trunk lines
Logically, whatever subnet the NVR is on, cameras also on that subnet it knows to scope out over the LAN port and not restrict to the PoE switch built in. This should work without any issues solely based on CCTV networking alone. If you plan to do anything beyond the IP cameras as far as networking is concerned, this is not the most preferred setup by any means... but it DOES work.
But I do not have any routers or any network of any sort in my house or any other devices to plug in. Therefore the uplink from the NVR will not be needed? Do I really have to have a switch in the house if the NVR is my sole network heartbeat?
Yes. You want to take advantage of GigE speeds for any and all trunk lines, and the NVR only offers that on the dedicated LAN NIC. PoE switch is FE and nothing more. Seeing as it only has one Gigabit NIC, and you're going to have more than one trunk line (1 per building), a switch of some sort, whether standalone or built into a router, is required to "split" the Ethernet line from the NVR to each trunk line. Technically, if you can solve the Fiber/Copper media conversion, those switches you got from work will be fine, so long that they are gigabit. They looked old so perhaps not.
So to help me be clear in my own head, my NVR will be my main network switch/hub, brains of the operation? correct? and it seems with a monitor or a flat screen TV hooked to my NVR, and either a mouse or remote that will let me control my NVR, it will be stand alone?
Brains of the camera feeds, yes. Network? No. You'd basically just have a bunch of devices connected together talking to each other on the same wavelength. There is no center piece because you don't have a router with DHCP, DNS, etc. It's all just there, and that's it. If you want it standalone with no remote access whatsoever, that's effectively how it works. Even if you did have a router... NVRs, cameras, or anything that is hosting a service you're generally going to want static. All it takes is one DHCP lease renew cycle and another device could snag that address, and you're left to find what it changed to. Not the most pleasant experience in the world.