+1 for Mikes suggestion.
You'll want the 750e outdoor system. I have 4. They cost a tad bit more and run on a windows PC. The night vision is pretty good for animals that will come a stand around a bit but anything moving is a blur.
As Mike said, you plug it into your home outlets and video / sound comes through you home wiring, then you'll need and outlet at your PC to plug another box into, then that plugs into a router for its trip online and your PC.
You can view from any PC on the web via website Logitech has. If you needed it a ways out from your home you could run a drop cord. My house is 40+ years old, so I ran a dedicated 110v line.
As for taking photo's its not that great. Just for watching them and recording for watching later, you can't beat it for the price. It will send you text alerts, play desktop alerts, send photos and can be viewed on most smart phones if you have Internet access. The built in mic is great. Every night I come home and put on headphones and have the camera's on a second monitor. I can hear cats walking by and all sorts of crazy things in the woods I sometimes never see.
Your point n shoot would work if they can be fired remotely. I set up the camera outside with flash. Watch with the Logitech and when something gets where it needs to be, I fire the camera with a remote. But this is getting pricey.
The low cost way to get photos of wildlife at night is a trail camera. Here is a cheep one, the price goes up from here.
Set it and forget it. Go swap the memory card the next day and see what you got. This, even a better one fits your budget.