If we ignore the option of utilizing a card, how much circuitry would be required to use a VGA chipset in the computer itself? I.e., include the VGA chipset as part of the "motherboard", so to speak?

Using VGA chipset as a part of motherboard won't need too many components but for doing so you will require implementing ISA or PCI bus as all these on board graphics chips which are seen on most of PC mother boards use such buses. Implementing such a bus would again ask for higher MIPS for example PCI is a 33MHz bus and would demand really high atleast 33MIPS+ micro.

If you want to implement a VGA driver using dedicated 8051 derivative then for 640*480 resolution with 8 bit color depth & 60 Hz refresh rate you will need 30MIPS+.

What ever way you chose the core trouble remains the same i.e. speed of 8051. In my opinion a FPGA should be used. or use a big Color GLCD screen.

Regards,
Prahlad Purohit