The only camera brand I have experience with is Axis Communications (very, very nice cameras, but very, very expensive too). There may be more options now, but back when I was playing with them I was able to configure the camera to record to a Samba share (instead of, or in addition to recording to an SD card).
I also have setup the server that grabs those recordings to sync with a VPS through Syncthing, along with an encryption key that the VPS doesn't know, so it only hosts an encrypted payload. If I need to retrieve the recording, I can simply add another host to the VPS and input the encryption key on the new host and it will grab everything decrypted.
The cameras are mostly meant to give me warning of someone breaking in while I am home and give me situational awareness across the house in the event of an entry.
Push notifications while I am away or being able to review people casing the place or such are bonuses.