Personally, like others I would recommend a 1440p IPS LCD monitor with at least 120Hz refresh rate & also at least FreeSync support, though I would recommend G-Sync instead if you are getting a Nvidia video card.
But lets make things easy for the sake of you, your budget & your comfortability level. If you don't care about high resolution or high refresh rate or both, then stick with the monitor you have now which I assume is a 1080p monitor with a refresh rate of 60Hz. Then go for whatever beefy video card you can afford, the more powerful the GPU, the longer it will last you without needing to upgrade. With that, you could crank the shit outta the graphical fidelity to the max with including Anti-Aliasing of current games as well as many upcoming games. And that's it. The only possible limiting factor in bottlenecking your performance few years down the line could be your Intel Core i5 & maybe your RAM which you did not specify it's capacity but if it's at least 16 GB RAM then you should be fine.
If you disable V-Sync, you could achieve a much higher FPS than the limitation of your 60Hz/FPS monitor to the limit of what your CPU, GPU & to a lesser extent, RAM can output. But this will introduce heavy screen tearing specific to your monitor. If you enable V-Sync, the visual output of your GPU will lock itself to your monitor's 60Hz refresh rate & output only a maximum of 60 FPS & will eliminate or at least reduce screen tearing as much as possible. This however, will cause input lag but as for how severe it is depends on your setup, your rig & your perception. A FreeSync & G-Sync supported monitor could reduce input lag to possibly being unnoticeable. Another minor issue is bottlenecking the full performance of your rig but that shouldn't concern you for too long as future games get better & more demanding, you will be getting more worth out of your rig you paid for. I call that future-proofing.
Hope you got the gist of it.