Now I'm very new to arduino and have trouble figuring out which is the best arudino board for my project so if you can suggest any boards and extra hardware that are compact in size that are essential for my project then pls let me know!
You need to get something working, first, THEN figure out how to reduce the size.
that is able to detect fast moving objects on a screen; computer/lcd type screens and be able to detect the color(s)
This is not a trivial task. You will need a large array of sensors, so that you can detect movement. Unfortunately, that large array of sensors will take time and memory to read and store the results. The time is not conducive to "detect fast moving objects" and the memory usage does not fit well with Arduino (which has limited memory).
What game is generating these "fast moving objects" and what are you sending data about them to?