Go with Unifi then. They're pretty much the only network equipment company with good software. The NVR (the computer that records/stores the camera feeds) can be used with or without internet access. If you know how to setup a VPN, you can connect to it without giving it internet access. If you don't know/want to do that, you can use their free web portal to access it remotely.

Cloud key G2 (NVR) is ~$200 and includes a 1tb HDD, G3 Flex cameras are ~$80 each. If you want to save some money, you can skip the cloudkey and install the software on an existing computer on your network.

All you need for wiring is to pass a single ethernet cable to wherever you want to place the cameras since they use PoE (power over ethernet). You'll also need a PoE adapter for each camera if you don't have a router that supports PoE. They also sell really awesome routers and switches with PoE, but if you're new to PoE be careful and do your research because it can permanently damage incompatible equipment. The older EdgeRouters are an incredible value, but the PoE variants use a non-standard and more dangerous PoE implementation than the newer ones. The EdgeRouter X SFP w/ included power adapter does work fine with G3 Flex cameras though, since that's exactly the setup I have (I don't think it'll work with the Cloudkey G2 tho).

...also yes, I'm a bit of a fanboy.