A Dual or Quad core processor is recommended for high video quality and speed.
Windows 7 (32bit or 64bit).
2GB or more recommended for high video quality.
A high speed web connection ADSL or cable (1Mbs upload speed is recommended for high video quality and fast frame rate).


Apart from the computer quality the available bandwidth is critical.
When running mega pixel and HQ cams you need a dual or quad core processor. I say dual as they are more common in current laptops as opposed to quad cores.
Windows is necessary (unfortunately) for most (if not all) cam broadcasting programs, splitcam and the majority of cameras.

Toshiba makes one of the better laptops but I don't think there is that much of a difference between major brands.