guitar333, excellent link!
The battery question depends on what you want. If you want to run your stereo/computer with the engine off, until the battery dies, but still be able to start again afterward, then do the battery isolator.
If you want to run the stuff with the engine off for twice as long, and don't care if the car will start afterward, then wire them in series.
If you want to run your car the whole time, then you don't need an additional battery...as long as you shut off your computer before starting the car.
My truck has 150A alternator... 150x12=1800 watts of output...I am not using a hair dryer, nor am I trying to broadcast music to a stadium, so that is enough for me.
Since the poster wants to run the computer off a separate battery, then the battery isolater is the way to go.