yes that monitor will be a great solution for you to hook up with your ps4. I myself use a 24" 1080p monitor with my ps4 and pc. The speakers will work with the ps4 as long as you hook up through HDMI, which you have to do anyways
I am not sure of the input lag on the monitor, but the 2ms response time is pretty good so motion blur should not be a problem for you.