I use two different systems to achieve what you want to do.
I have a Reconyx Hyperfire 2 cellular game camera which I mount at the entrance to our 500' driveway when we are away. It takes stills and video of anything entering the drive. It alerts us on our cellphones which we can use to view the incident. It's high def pics can easily read a license plate. There is never more than a 20 second delay although this can vary depending on your location and cell provider. We use it as a game camera when we're home so it serves a dual purpose.
www.reconyx.com
We also have an outdoor Nest Cam mounted on the garage within WiFi range. It has a clear view of the drive and anyone approaching the house. It also notifies our smartphones with pics and video when triggered. It auto zooms in on faces to aid recognition. The delay averages 20 seconds. It stores the images off site and can be reviewed for up to a month.
Both cameras require a subscription. The Nest cam costs $137/year which can be reduced or eliminated depending on the storage duration desired.
The Reconyx cam costs $16/month but can be activated only when needed.