Thanks for the replies guys.
I'm not stuck on any choice (including AMD vs Intel) nor the budget yet. I initially "picked" the 1920X from the list on PCPartPicker because it looked like the 1920X had a good number of cores and a reasonable speed for my needs and the price is very good. So it seemed like a good starting point for a discussion.
There is a 2920X that's a generation newer and about $400, but from what I can see the performance difference isn't significant compared to the 1920X, while the cost is about double (hence why I figured the 1920X was a reasonable starting point).
As far as the budget goes, I want to keep the cost "reasonable", but am also able and willing to spend what I need to within reason to end up with a system that will work well, hopefully for 5-10 years without needing any major upgrades in that time (other than maybe a newer video card). So I'm willing to spend perhaps ~$500 on the CPU if there's a good reason to do so, but I'm not willing to spend $1000 or more on a CPU, which rules out the current 3rd generation ThreadRipper options, for example. Similarly, I'm not opposed to spending as much as $400-500 on the motherboard if there's a good reason to. But I'm also happy to spend less and hold on to the leftover money.
For the OS drive, I'm planning to use a Samsung 860 EVO 500GB SSD that I recently upgraded the old system with (I needed to update the old OS drive as I didn't have enough free space left to install the Windows 10 1903 update). I had been using an SSD for the OS all along. Getting a second one and running them in a RAID is an option, but is the slight complication in the setup really going to provide a big benefit?
The separate network card is primarily to avoid issues with the SiliconDust HDHomeRun tuners:
I had been running into problems with dropouts in my TV recordings on the current system that ultimately were an issue with the integrated LAN on the motherboard (which uses an Intel LAN chipset). After quite a bit of effort in trying different drivers, tweaking the network card configuration and so on, installing the separate Intel LAN card resolved the issue. SiliconDust has a command line utility that will report any network issues and it was reporting lots of issues with the motherboard LAN, but none with the add-on card. A big difference with networked TV tuners versus other network activity is that there's no opportunity for a retry as it's essentially a live stream - you either get the data on the first try or you don't get it at all. For the home network, I'm using several HP ProCurve Gigabit managed switches (48 port in the basement rack, 24 port in the home theater room, and a couple of 8 port units in other rooms) and a Ubiquiti EdgeRouter 4 as my router.
I had also tried running the BitTorrent client on the PC alongside JRiver and found that it caused TV dropout issues when it was active even with the add-on LAN card. I don't use it a ton, but when it's downloading something, it can use a lot of network bandwidth. I've got Verizon FIOS Gigabit service at the house, so something like this can come close to consuming most of the bandwidth on a single Gigabit LAN connection. So I definitely want to isolate that in a separate VM and separate LAN connection, or continue to run it on a separate PC.
It's possible that on a much newer system some of the network issues I had run into won't be an issue, but newer hardware won't make a single Gigabit LAN port provide more bandwidth
.