We have a Blink system we’re pretty happy with, that includes several cameras around our house, including a doorbell camera. Each individual camera is fairly inexpensive and modular (so you can add and subtract cameras as you like). The cameras, including the doorbell camera, are wireless and battery-powered so no need for doing any wiring. The batteries in each camera last a long time, like a year or even two.
You view the cameras through an app, either live, or it saves brief video clips when motion sets it off. I’m 99% sure the online service does not require a monthly subscription cost, though I’ll have to ask my wife to make sure of that. We got Blink before they were bought out by Amazon though, so we may be ‘grandfathered in’ on the lack of monthly subscription costs.
Be prepared for lots of false positives on motion detection. Wind, rain, blown leaves, critters walking past…
Let me know if you have any follow-up questions.