I chose a wireless camera system, with a local DVR that I can access via PC or mobile. You can, if you choose, feed those cameras into different software programs and have all the motion sensing and advanced config you'd like.
That might be more than you want to setup, though, and if that's true, there's some packages that sell DVRs with those same features. My sister, who isn't very tech savvy, has managed to do all kinds of things, like masking parts of the room from setting off motion detection, with the packaged software.
Anyhow, I'd start off with the search feature.
Lots of good threads above. I personally use a bunch of cheap Annke (rebadged Hikvision?) cameras along with Blue Iris. It is great, but a lot of work to maintain.