You don't need much computer. The catch is storage. If you store larger files and more of them.... you need more space on good drives.
Once you start using filters it changes things a lot.
First layer of filtering is motion detection. You 'paint' an area of interest that you want triggered on motion. You can tweak it like crazy, including things like object size. But, plain old motion detection still triggers a lot of falses (wind blowing trees/bushes for example). I don't alert on simple motion detection.
The second layer of filtering is using AI object recognition. Most of my cameras are set to scan for people/cats/dogs. If one of these is detected an alert is triggered (email and audible). I use different alerts depending on the zone, for example a front door alert triggers a door bell sound.
If you wanted you can also use facial recognition, so you'd only get alerts on unrecognized faces.
I only have 256Gb of storage, and I keep 7 days of video. It barely gets 5% used.
Some of my cameras also have a spotlight function, if they detect a person it turns on an LED spotlight in the camera (I use that as a deterrent function).
BlueIris operates as a web page (internal on your network). I've set it up so anyone with a PC/laptop/phone/tablet in the household as the shortcut. And in our kitchen I've setup a cheap 10" android laptop that has that camera page running 24x7. It has all 6 cameras thumbnailed, and automaximizes a specific camera on any motion detection.
There is a mobile client, but I simply use a VPN back into home on my phone to view it real time if needed.
The level of tweaking you can go to with BlueIris is nuts.