Question Which Monitor should I buy for my 120hz Laptop?

[unknown_99]

I have an ASUS FX505GM-Q72S-CB 15.6" 120 Hz, I am planning to buy a monitor for a better gaming experience. So what should the monitor's hz be? and my laptop can connect only via HDMI(version not written). If I buy a monitor that is 60hz will that affect in any way?
Thank you,

 

[Deciplox]

My personal opinion would be to purchase a 144hz monitor. (get the most out of your laptop).
In regards to the MS it would not matter too much whether you get 1ms or 3ms.