Coincidentally I'm upgrading our CCTV right now (partly prompted by some walker whose dog savaged one of our hens).
We already have five analogue cameras so the new setup needs to be able to handle those. However, they are dead in the water nowadays and IP cameras are the future, so somehow I need to allow for those as replacements. Don't need (or want) offsite access but do need remote display, PC display and mobile (but restricted to LAN).
I've just installed a Dahua XVR (a just obsolete model, so reasonably cheap at £80 without storage) which has notionally 16 channels but can go up to 24 if you make 17+ IP cameras (and lose IVS). Any combination of analogue/IP with the only restriction that they are all bunched together, with analogue first. So you could have cams 1-4 analogue, 5-16 IP. Or 1-13 analogue, 12-16 IP. Etc.
Display is either VGA or HDMI. The previous setup had VGA locally and coax to the remote screen, but that was over UTP. With the new one I could use HDMI locally and VGA over UTP to the remote display. But instead I picked up an old IC-Stream64 which is essentially an NVR without storage and intended for exactly this purpose.
The Dahua handles both types of camera very well. With IP cameras it can do PTZ if the camera has it built in. Talking ONVIF seems to be best, but it's picky - an old Keekon which can be views with many ONVIF utils isn't seen by the Dahua.
So far as Internet access goes, none is required. Even the official Dahua mobile app can work entirely locally. The NVR has a built-in firewall so you can ensure only local addresses are allowed (although, given the source, I wouldn't trust it not to do a google and allow certain parent addresses on the sly). There is a P2P mode which sounds dodgy, but so far as I can make out it allows remote access without having port forwarding. The NVR and remote station contact a central server which connects them together and then gets out the way, so it's not P2P as you might imagine file sharing, nor is it cloud like Netvue. Still potential for some third party to sneak in if your password is rubbish, although you aren't allowed to use a stupidly simple password.
Just also noticed that because it talks ONVIF it can be embedded in Home Assistant (although the frame rate is about 10s/frame, unsurprisingly).
For a startup system I would be inclined to go all IP from the start, but IP cameras with decent lenses (that is, zoomable for use over more than 10') seem to be rare or expensive. You can still get the analogue ones with 270x zoom (27x optical) quite cheap, so a mixed system might be preferred.