I use Samsung U32J590 and old Samsung TV. I know that max resolution for Intel HD 530 is 4096x2304@60Hz, but unfortunately it can be achieved only using Display Port, which my motherboard (ASRock Z170 Gaming K4) doesn't have. Otherwise max refresh rate is 30Hz for 4K resolution.
It's difficult to determine the exact budget. I don't want to spend more than 300PLN, which is about 75USD, but the fewer is better.