Update: Tried lowering the graphical setting and, while the game did run a lot smoother, it didn't help with the crashes at all. Also is worth noting that the severity of the crashes go from a simple crash to desktop to a complete lock of the system, which happened right now.

My computer yielded this report after rebooting, if it's of any help:

Firm with problems:
Name of the problem event: BlueScreen
OS version: 6.1.7601.2.1.0.768.3
Regional configuration Id. : 2058

Additional information regarding the problem:
BCCode: 3b
BCP1: 00000000C0000096
BCP2: FFFFF8800BAADAB7
BCP3: FFFFF8800DBE0C90
BCP4: 0000000000000000
OS Version: 6_1_7601
Service Pack: 1_0
Product: 768_1