In theory you can have cameras at home and at business and have one computer running Netcam Studio (NCS) at home. However, practically this will not work unless you have a very good high speed connection between business and home. IP cameras send video and depending on the resolution of the camera they use quite a lot of speed in the network. Assuming that you have a normal Internet connection between business and home I suggest you have one system with computer, NCS, storage and cameras at the business and the same setup at home. This will work directly and give you least problems.
If you want to see your business cameras at home you can use the webclient ot mobile app or you can also connect NCS(business) with NCS(home) and have all the cameras on the same interface. The FPS for business cameras will be rather low, but that is not a problem.
Be also aware of the high resolution cameras (2, 3, 4 … megapixel) need a lot of computer power for the whole system to work properly.
Computers running NCS must always be on to record.
Since the cameras will be on different LANs you must at least now the public IP for the internet connection to your business.
If you hesitate for another computer, don’t buy a new one. I always buy computers that are about 2 years old. You get so much more for the money.
This sounds like a fun project and rather straightforward as I see it.