We're probably looking at a 14" laptop. For a good compromise between screen size and portability.
How well built are you from the strong as an ox to the dainty waif type build?
A 15.6" or 13.3" laptop might be perfect for you - depending.
It would be nice to get you an 11th gen or later Intel CPU, or one of the more modern AMD CPU's to give you more flexibility on the games it will play well.
I also prefer laptops with slot-in (non soldered) RAM and SSD's. And it's a nice bonus if the laptop can take more than 1 internal SSD.
Ebay's the place for the best deals on laptops.
The right used business laptop at the right price will be a great tool for your computing needs at uni and beyond. I can suggest a few specific deals once you've told us a bit more info on your mobility profile.