EDIT - Modified this answer slightly (now three parts)
Low Budget Version
Pick up a used router (laying around the house?), install dd-wrt on it and turn off the WiFi. Bingo, ready made 4 port switch. You won't get PoE for the cameras, but, if needed, that's easily rectified (pun intended) with a PoE adapter or just wall warts. Run a VPN on the dd-wrt router, put it in the main router's DMZ (or port forward) and you're good to go. No Linux management, if you really don't want it. Cameras are isolated from the home network and protected from the inter-webs.
You might go pretty far by picking up used network and camera hardware on the cheap. Raspberry PIs are wonderful devices, too, and can help run a network.
High Budget Version
My current setup for comparison purposes. I currently own five Axis cameras for my home security system, powered by a Cisco PoE switch and fronted by a Cisco router. Much more than your parents want to spend. However, I think the model is good for you to consider as a reach. I engineered this set up myself with no prior network (IT) experience. It was a learning moment, for sure.
The biggest concern you'll have is the one you're already worried about, hacks from the Internet. This is best solved with a three pronged approach.
First, the better the hardware facing the Internet, the more secure it will be.
Second, harden whatever you've got facing the Internet and sitting inside (change all default passwords, close unneeded ports, run a VPN rather than UPnP, if you can). Isolate systems from users, if possible (i.e., if you have a switch, put the cameras on a vlan).
Third, scan your hardened network with nmap from the outside and use www.grc.com from the inside. GRC is a great starting point. Use nmap from the inside, too, to see what ports you've left open internally that might create future problems.