The right display resolution is a mix of preference and performance reasons.
Usually the resolution to go is still 1080p (1920x1080), if your monitor supports it and you have an high end system, you might also be able to play on 1440p.
At least in the beta right now, Black Ops 4 isn't running that great though. Even on high end systems with a 8700k and a 1080TI we saw deep drops, even under 144 FPS.
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On 1080p and all low that is.
So, if you have a lower to mid-end system, you might want to go on a lower resolution for more FPS. 1600 x 900 is a popular option, if you want to stay on a 16:9 aspect ratio.
If you can spare some screen estate on the left and right, you can also go with a 16:10 resolution like 1400x900, saving another 15% pixels that need to get rendered.
4:3 in Black Ops 4
If you're really old school or need even more FPS, you can think about playing on a 4:3 resolution like 1280x960.
To get the right aspect ratio or make it stretch via your GPU driver, you need to set the aspect ratio in the config file. 4:3 is currently not supported in the menu, but the game itself supports it.
Setting 4:3 in the config file
Open the config.ini which you can find in the /players/ folder in your main Black Ops 4 installation directory.
Find the aspect_ratio command and change it to 4:3, so it looks like this:
And you're done. Enjoy 4:3.