The entry point for a lappie capable of playing games is about $850 US. As for the coursework, id consult with the IT department at university and ask about coursework needs thru obtaining a degree as you don't want to have to replace next year.
I would also recommend having a custom laptop build to the necessary specification as a less expensive and higher quality alternative to store / e-tailer bought options where you have no idea whoa ctually built the laptop. Of all the brands you migfht recognize, MSI is the only brand that actually **makes** a laptop.
The vast majority of laptops on the market (94% in 2011) are manufactured by a small handful of Taiwan-based Original Design Manufacturers (ODM), although their production bases are located mostly in mainland China. Major relationships include:
Quanta sells to (among others) HP, Lenovo, Apple, Acer, Toshiba, Dell, Sony, Fujitsu and NEC
Compal sells to (among others) Acer, Dell, Toshiba, Lenovo and HP/Compaq
Wistron (former manufacturing & design division of Acer) sells to Dell, Acer, Lenovo and HP
Inventec sells to Toshiba, HP, Dell and Lenovo
Pegatron sells to Asus, Toshiba, Apple, Dell and Acer
Foxconn sells to Asus, Dell, HP and Apple
Flextronics (former Arima Computer Corporation notebook division) sells to HP