If you want to play anything over 4K 60hz ideally you want something with HDMI 2.1 and there are not many on the market yet. I'd recommend the 144hz 27GP950 which is over your budget at £750 if you get lucky enough to order one.
If you only want up to 60hz when I believe anything with HDMI 2.0 should be fine. Anything HDMI 1.4 would be limited to 30hz at 4K.
HDR 600 is alright, I've not played on anything less than that. Up to you if you care about it or not, not a deal breaker not having it IMO.