Can you further explain why you think the HTPC needs a GPU upgrade? Is the 280X not cutting it for the kids? Only reason I ask is because it has the potential to steal budget from upgrading your PC. FWIW, a 280X is roughly proportional to a GTX1050Ti/RX560 (possibly a smidge better than those cards, but closer to them than a 3GB GTX1060 or RX570).
Your gaming PC with 7850 could definitely use an upgrade, so it's best prioritize the upgrade dollars to get that up to speed. Not sure what your budget is since you've mentioned both a $260 and a $560 GPU in your posts.
I personally own an RX480, so my research lies in FreeSync monitors. I know that G-Sync monitors generally
tend to cost more for the same features as a FreeSync monitor. I have some "moral" oppositions to G-Sync which does sway my GPU preferences despite considering myself manufacturer-neutral (my last GPU was a GTX660 and before that was an AMD 6850). I like what AMD is doing with their software (overall software functionality, Framerate target control & Chill, enhanced sync, Wattman, etc etc) but they've been "plagued" by supply shortages from the cryto-mining craze earlier this summer so their price/perf ratio were a bit off, but prices are settling back to normal levels now.
I like 27" 1440p monitors for their size and resolution (109ppi vs 92ppi on a 24" 1080p monitor so it's a similar look. 27" 1080p is too low ppi for me). Something like a RX580 or GTX1060 can do 2560x1440 @ 60Hz with high settings on most games. Certainly a Vega56 or GTX1070Ti would give you a little more power for future titles though. The Nixeus Edg27
has been on sale a couple times at $400 and will probably be that price black friday week. The Samsung C27HG70
has been as low as $490 which is a great monitor also (despite the stand being wierd)
Something else to consider are 29" ultrawide monitors. The LG 29UM69G
is a 2560x1080 IPS panel and has a 40-75Hz FreeSync range. It's been on sale recently for $230 ($210 on ebay) which I'd expect it to hit again on black Friday week. My brother has the older 29UM67P and it is a good fit for his RX480 (for reference UM67 was 60Hz fixed refresh and 40-75Hz FreeSync, the UM68 upgraded the panel to native 75Hz fixed refresh and 40-75Hz FreeSync, and the UM69 added USB-C and a ?height-adjustable stand?). A 29" ultrawide monitor will be roughly the same vertical height as a 24" 16:9 monitor, but the ultrawide will give you an extra 5-6" of width.
There are frustratingly few PC games that offer split-screen multiplayer.....
Main: i5-3570K, ASRock Z77 Pro4-M, MSI RX480 8G, 500GB Crucial BX100, 2 TB Samsung EcoGreen F4, 16GB 1600MHz G.Skill @1.25V, EVGA 550-G2, Silverstone PS07B
HTPC: A8-5600K, MSI FM2-A75IA-E53, 4TB Seagate SSHD, 8GB 1866MHz G.Skill, Crosley D-25 Case Mod