Just leave the car running, or have a battery charger on if at home, when playing with stereo.
Normal batteries are fine, dont spend more than $100, and get something with a decent warranty.
Dual battery systems aren't worth it for anything but show cars, cruisers etc. due to extra weight it would add to something like the GTR.
Perhaps a heavy duty low voltage cutout would be a good compromise.
Anything under 10V = battery death, you may be fine, or you might not.
Don't be suprised if it works fine for a few months then dies unexpectantly.