With the GTX 670 all of those will be underpowered. A 720p @60 Hz might give you a solid 60 fps.
If your goal is to barely keep above 30 fps which has been said to be the minimum for "playable", then a 1080p @60 Hz would give you a crisper image. Getting a 144 Hz monitor for showing a slide show, well, you know the answer.
Your best choice would be to get a newer, faster video card and think about the monitor after that. For 1440p @60 Hz a GTX 970, 1060, 1660, 2060 are plenty good for AH. For higher speeds 980, 1070, 2070 or higher are able to unleash the power of 144 Hz.
If you're on a tight budget, a used 970/1060 will give you a solid performance on 1080 or even 1440 @60 Hz.