The most effective BC rush would be one on a map with Forerunner Reactors.

I go Temple (build Brute then recycle Temple), WH, Hall, WH, WH, SG.  Grab a Reactor, and now you have the extra 500 from recycling and you're set for a steady flow of Brutes, Hunters, and Jackals.  It's very easy to overwhelm your opponent.  Keep threats at bay with Vortex if desperate.  It has its counters, but works against a lot of strats.  Use Brutes vs buildings and Hunters/Jackals/Vortex against enemy units.  I haven't lost with it yet.  Though, I have only played about 10 games with it.

No hero upgrades with this strat.  You can't maintain a flow of Brutes, Hunters, and Jackals if you blow cash on upgrades.