to get the most out of it, you're gonna want a 4K monitor with HDMI 2.1 and HDR. but a monitor with all these features is gonna be expensive ($700-1000+)
GSYNC and FreeSync are variable refresh rate (VRR) tech for PC's, so you won't need those for your console. the PS5 uses HDMI 2.1 for VRR, but Sony still hasn't released an update to support this (it's supposed to be coming). you also don't want any kind of 'ultrawide' monitor, since the consoles won't support that either. might want to avoid a 1440p monitor, since the PS5 doesn't support that, and will most likely only give you a 1080p image (although I guess some monitors can
trick the PS5 into outputting a 4K image, and downsample it to 1440p. do your research if you go this route)
like I said, a monitor that really uses all the PS5's features is gonna be expensive. to the point where you might be better off just getting an OLED TV. but if you're willing to sacrifice some features, you can go with a cheaper monitor. IMO the first feature to cut would be HDMI 2.1, since the PS5 doesn't support that yet, and most games probably won't use it when support does come. next would be HDR, and then resolution. you definitely want something with low input lag (1ms). even though I said the consoles don't support FreeSync, you will find it's a feature on many monitors, and you'll still be able to use any monitor that has that
best cheaper option IMO would be something 4K and 60hz from a good brand (Asus, AOC, Dell, etc)