What are good options for self hosting home security camera?

I’d like to host this on the Ubuntu Linux box in my home office and put a camera in my living room. Would like to be able to monitor the camera from an iPhone, and have it auto record on motion detection.

For external access though, I don’t have a domain name registered, and I’d rather not have one. I’d be happy to access this just using my external IP address. But I don’t know how “static” the IP address from my ISP is. (My router gets it via DHCP, but I don’t know how long those leases are, or if it re-uses the same IP when renewing.)

Edit: Also what is a good camera to use? Seems like a lot of these cams require registration with some shady service and their own app to view them. Which means that all of that is running through their hosted service, which I am trying to avoid.