If you use Ring, assume that a couple of thousand Amazon employees will be able to monitor your cameras, both audio and visual. There have been lawsuits and congressional inquiries about snooping, and every statement Amazon has ever made has been carefully worded to reference "unauthorized" monitoring, or "access to that data exceeded what was necessary for their job functions." Seems to me they're pretty much on the honor system. And while my first thought was just to install a second router to give it wifi without internet access, the devices are pretty much bricked without cloud access.
Also, if you don't care about Amazon goons snooping around, for Gods' sake set up a challenging password and two-factor authentication to keep the pervs out. They're probably a bigger threat than Amazon.
Moreover, I don't know if you have any regard for this or not, but also be aware that Ring is a massive surveillance clearing house for law enforcement. While most wouldn't care, the civil liberties part of me finds it rather repugnant.
Lastly, two adages apply here. A: If the product is free, you're the product. Amazon is getting something out of all of the cloud processing that goes into this. B: You don't own your information. Any surveillance picked up by Amazon belongs to them, and they're free to do whatever they wish with it.
edit: Oh, and since you did ask for options, it's certainly possible to assemble such a system yourself, which gives you all of the control and leaves the cloud access out of the equation. For a while I had webcams pointed at both of my doors which would send pics to my phone if any movement were detected. It'd take a little more effort than just ordering a package from Amazon, but it's hardly rocket surgery.