(C) Both of the above, maybe.
I've seen enough grainy nighttime videos to realize that identification is iffy at best. You get a wonderful record that some unidentifiable scumbag was trying all your car doors... and that's about it. And I've seen a few local videos where the individual used a bandana to cover his face - obviously knowing that the camera was there but not caring otherwise. I assume the police don't get much out of the recordings, unless it corroborates some other data that does identify them.
But if I'm going to spend the money, might as well get something decent. Proving that some delivery guy threw your package 15 feet onto the porch seems like a useful option, for example.
I know cheap dummy cameras are a thing. Not sure how much a deterrent they are if people ignore the real ones too.
While there's no way cameras can guarantee you catch the perp, a well-designed system can help develop an ID.
You probably want something to capture a license plate. I don't know your driveway layout but you'll want a camera with a high pixel count at whatever distance you feel is adequate. For instance, if you live on a street and get a camera that only illuminates (via IR) 10' of your driveway, you won't get a good shot of the license plate of the car parked on the street.
Another aspect is to view the areas that may invite a perp. Your front door/porch, back door/porch, AC Unit, etc.
And another is audio. Do you want it?
You need to determine your field of view, target height, and install height. For example:
- You want to mount a camera at the corner of your 2 story house (let's say 20ft) aimed at the end of your driveway that's 30 ft away and you want a 55-degree field of view.
Next is to determine the number of pixels you need per foot. I would use a minimum of 38px/ft.
Axis is a great camera mfr. and they have this tool to help select cameras based on all the criteria above. (Disclaimer: I don't work for them, I just use them in security camera designs)
https://sitedesigner.axis.com/
They are also very expensive. The hypothetical corner-mounted camera above would use an Axis Q3515-LV. That camera is about $800. For one camera. You can use the camera data to select a cheaper one though.
You'll also need to determine the camera type. IP or analog? I'd go with IP and Power over Ethernet (PoE). That way it's one single netwrok cable from the DVR to the camera.
Speaking of DVRs, once you have the number and types of cameras figured out, you'll want to decide on storage. How long do you want video stored? Maybe you go on vacation for a week without WiFi or cell service and don't get the notification from Nest or Amazon camera and the video is lost. Then what? The higher pixels per foot, the larger the storage needs. Not to mention data rates, PoE power, network ports, etc.
I'm not trying to inundate you with information, I want to point out that there are a TON of options out there, as you probably saw, but designing a real CCTV system requires time and some thinking. Don't be suckered into marketing gimmicks like "1080p!" or "15MP" without knowing what you want and why.
If you want something simple and easy, certainly go with a Nest or other simple camera, but be wary of the storage. they may charge you to store or what you can store for free isn't very much (going back to the vacation hypothetical).
Good luck.