Whatever your opinion may be on Ring and privacy, the Ring 2 at $90 is a really good deal. B&H has it on sale today: https://www.bhphotovideo.com/c/product/1382047-REG/ring_8vr1s7_0en0_video_doorbell_2.html
I would get the ring pro; these don’t always work well on batteries.
Sure, the Ring Pro is better (and more expensive). But if you don’t have the wires to power it, the Ring 2 is as good as it gets.
The Ring 2 Doorbell also works just fine hard-wired to your existing doorbell transformer. I have had mine installed for a few years now and it has always worked reliably.