personally, i feel that budget is a big factor, especially with students.
I would go for a laptop that has long battery life, has the ability to transform into a tablet, and with a decent CPU (minimum 4th gen i3) and 4GB ram. i wont need a laptop with a dedicated GPU because the integrated graphics in the i3 processor is good enough to run most games (few years old) at low settings eg. dota 2, counter strike. i will instead invest in a desktop for serious gaming. the price of a gaming desktop + a working laptop is lower than a gaming laptop. as a student, i want to be more budget conscience.
i need long battery life because when you are in school, you move around all the time, meaning you will likely be without a power point most of the time. You cant afford your laptop to die out on you. the ability to transform into a tablet will help me if im in a scenario whereby i need to carry the laptop. i cant possibly type on the laptop while carrying it. the i3 processor and 4GB RAM will make sure that work done on it will be smooth without lag.
so main thing im looking out for is: budget -> battery -> processor -> ram.
if got more budget, definitely a SSD instead of HDD. working on it will be even smoother. faster read write etc.