I would recommend a variable refresh rate (Freesync or G-Sync) first as it will smooth out games regardless of frame rate. Within that category I'd go for the 1440p 120Hz or higher monitor. If you have the video card horsepower, use upscaling to run at 4K in games that look better with a higher resolution (I actually run Black Desert Online at 5K using a 1080Ti because it smooths out some artifacts in the game). Upscaling won't give you a perfect 4K experience - but it is close unless you are extremely sensitive to a monitor's pixel pitch.
Using a 1440p monitor will help avoid scaling issues with Windows and the apps that are poorly optimized for 4K. But, really, you would do well to check out monitors at a local store if you can before you decide, you might find a 4K Freesync or G-Sync monitor is better for you than my suggestion. And if you buy locally you can return the monitor more easily should you decide to go a different way.
There is also the option of saving money by going 1080p and using upscaling, but that doesn't work for me, the pixel pitch annoys me too much. Many enjoy 4K upscaling on a 1080p monitor though.