I'm not sure that namanjohnson101 is wanting just a PC based recording scenario, by alluding to
and the system will handle everything from there
ability to flip through channels and watch TV on three other TV's located throughout my home without interfering with the automated recording system ... able to tune in to multiple channels simultaneously (on the recording system and normal usage throughout the house)?
It's almost like a network-centric PVR is being asked, for recording centrally and watching on multiple networked TVs.
As you allude to, there has to be a way to "cast" videos from the central video storage server (NextPVR based in your instance) to the TVs, so a Firestick or Chromecast or whatnot in every TV (and the means to control it) would be essential ... assuming LAN networking or WiFi (a large capacity WiFi) is in place, and the TVs have the requisite HDMI ports etc (or, inbuilt in smart TVs say with WiFi).
Given the nature and wording of the "ask", I'd not necessarily be sure that all of the requisite underpinning infrastructure stuff would be in place (including decent new PC with a decent internal bus with bandwidth capacity to handle multiple simultaneous recordings to disks).
On a separate tack, assuming Australia and ignoring the $ - a retail, non-ISP-provided FetchTV Mighty (it has 4 tuners) on one "main" TV and with other TVs each having a Fetch Mini could be a lay-person's "goto" since they can all be interconnected and play from the central FetchTV Mighty ... assuming a decent capacity LAN/WiFi in the home. Subscription $6 per month includes a package such as BBC TV shows as well as the free-to-air TV channels as well as their catch-up websites like SBS-on-Demand together with access to a movies area (a bit like google movies). No ad-chopping, however the remote includes 32x fast-forward etc
I opted for 2x FetchTV Mightys on my LAN and haven't looked back

They are essentially 2 great big PVRs with a lot of extra features plugged into the HDMI ports of 2 TVs, so others can record what they want and I can record what I want without interference. These boxes can see and play each others recordings across the LAN.
Can also cast from my PC to Chromecasts attached into the TVs other HDMI ports if necessary, or, I find it easier to just walk around and plug in a 1Tb portable hard drive into the smart TV's USB port in the few cases where I have something like a home movie to play.