The monitor you purchase should have a HDMI port which should be common for all LCD monitor except for maybe the very least expensive ones.
I think your laptop only has a nVidia 840m. If so, then it is not a very powerful GPU. A monitor with 60Hz refresh rate should be fine since the games you will be playing on that laptop will very likely perform at less than 60 FPS; especially if you want to play any graphically intensive game released within the past 5 years. The refresh rate determines the max number of FPS the monitor can display. 60Hz monitors can display at most 60 FPS. 120Hz monitors can display up to 120 FPS.
Response time basically determines how it takes the pixels in a LCD screen to change colors. The higher the response time is the more likely you will see ghosting which can be annoying to some gamers. Your laptop has a TN panel screen which generally has 2ms response time. However, many gaming laptops have IPS panel screens which generally have 5ms response time and is generally fine for playing games.
Other than response times the difference between TN and IPS screens is cost and viewing angles. IPS monitors tends to cost more than TN panels. TN panels generally have poor viewing angles which means colors can easily fade as you tilt your head or the screen itself. IPS screens have better viewing angles where colors fade a lot less compared to the average typical TN screen.
Generally speaking, if the GPU is not powerful enough to push at least 80 FPS, then there is no real point in buying a LCD monitor with more than 60Hz refresh rate since you will likely not be able to tell much of a difference between 60 FPS and 80 FPS.