Just about any run of the mill DVR/cctv device such as a Night Owl DVR will work independently without internet access. These devices are not built like say a Ring doorbell where the device calls home over the internet to connect an app on your phone.
You would have to explicitly make changes on your firewall to open the device up to the internet. However you can hook up a monitor and mouse to the DVR all in one solution to monitor you security system.
If you really wanted to utilize your own computer (brick and mortar) you would have to get something like a 4 Channel PCI-Express card and an additional Hard Drive for storage and of course the cameras to connect them. Similar to a package such as this and this