Being a former student myself, I had upto 100 browser windows open. Sometimes you want those windows optional to you immediately.
My point is go for a laptop with atleast 8gb of RAM.
Any of the i series are good but I recommend the Ivy bridge 3rd generation. i3 and i5 are perfect even if you like to watch videos. But with an i3 gaming might be sufficient.
Also unfortunately the supply of Windows 7 disc remaining for retail sale are running out so they are all coming with ugly Windows 8.
I did a super super quick search on Amazon and I couldn't find a laptop with an i series CPU, 8gb RAM and 500+ GB HDD. (Although if you can ever afford it an SSD is a godsend - you can always upgrade later)
But here is a laptop with an AMD CPU in it.. AMD may be the compromise to having the other features but they are still strong. http://www.amazon.com/Toshiba-Satellite-S855D-S5148-15-6-Inch-Aluminum/dp/B00B3PFPOC/ref=zg_bs_tab_pd_bsnr_1
But take a look around