Then it's not just about Frequency then. I'd target a freesync panel, personally I like IPS panels.
What size were you thinking? I don't game much if it all anymore but I have two older teen boys and a girl, they game at mostly first person shooters. RB6 Siege, COD etc with some other stuff tossed in. The boys both like 24" 1080p freesync monitors for gaming the girl plays more stuff like Skyrim and WoW and uses a 27" 2K. The boys have RX 580's, the girl a GTX 1070.
4K is bit much for an RX 580, it will game most titles at 1440 with reduced settings though. Freesync is like a godsend when frame rates drop.