How can I implement a visualization of archived convective data from numerical weather models? I've always found geographic visualizations of surface/mixed-layer CAPE models and other weather data to be incredibly interesting.

Here's a map featured by the Capital Weather Gang over at the Washington Post, during the June 12-13, 2013 derecho series in the Ohio Valley/Chesapeake Bay regions. It was created by WeatherBELL, which is a subscription service offering visualizations based on their proprietary technology.

Here's another map featured on the blog of Cliff Mass, a professor of atmospheric sciences at the University of Washington. This is an internal UW WRF model that is GFS-initialized.

I would like to know how I can take archived GFS or WRF data and visualize it on a map. Or even if that's possible (perhaps archived numerical data is only available to paid subscribers). What I would like to do is plot surface and upper-air readings to better understand the mesoscale setups for thunderstorms in the Pacific Northwest, where I live.
The best model archive I know of offhand is Iowa State Meteorology's Gempak model data in their MTArchive.  Looks like model-wise, they have at least 10 years of GFS (and the predecessor, the AVN).  No idea if the models are complete files (include CAPE) or not, though.

Gempak software is free, though you won't get graphics nearly as polished as WxBell; they've spent a lot of time fine tuning their setup, and likely use newer more flexible tools (probably GrADS or OpenGrADS, both also free).  You could probably get GrADS to use the .gem files, perhaps by converting them?