I use the Unifi doorbell/cameras rather than Ring because I value having the footage stored on my own server rather than having to trust a third party.

call a technician to install the extra coax outlets

Just have the technician install Ethernet then.

MoCA is a great way to reuse existing coax to avoid having to run new wires. But if you’re going to run new wires anyways, then just install Ethernet.

Does the existing Uverse TV service use the coax in your walls at all? Or do you just get a Wifi box or something like that that plugs into your TV.

Have you done this before? What router did you use?