I am in need of your laptop buying skills!

Take everyone's advice: build a separate gaming PC and buy a less power laptop for studying. As for the laptop, I've always been attracted to very small and compact laptops such as Toshiba Portege series, but I'm not sure about maintainance issues as they are very small.

When they quote the memory for a graphics card, they mean dedicated memory. Cards in laptops that still use the AGP bus will utilise some system memory alongside its own dedicated memory when that runs low. This "aperture size" can be set by the user in the BIOS. If you wish to read more on it click here. I do not know how PCI-Express cards work in terms of memory sharing.

Do not be fooled by the size of the memory, which companies often use to fool unsuspecting consumers into thinking that more memory is better. The memory do not determine how powerful the graphics card is, but rather the clock speeds of the GPU, memory, and the number of graphics pipelines the card has.

Jam it back in, in the dark.