I'd say the marine v. auto question depends on how you use your boat. If it is stored outdoors or is docked for a significant time, I'd go marine. If you're a trailer boater who stores inside, auto should be fine. I'm the latter and went with auto and have had ZERO corrosion issues.
You can wire the power cable directly to the "out" on the battery switch and it will do just what you asked-only draw off the battery selected by the switch. If you use the power on/off connection that the amp will provide and hook it up to your radio head unit correctly, it will not draw any power if the radio is not turned on. In short, it only turns on when the radio turns on if correctly connected.
Best tip I can give you is to run the ground directly to a battery if possible with large gauge wire. If not possible, get an alternative to just tapping into the radio's ground. If you don't do this right you'll get interference/noise in the speakers.
Have you considered mounting the sub next to either the driver or passenger seat? That is where I did mine (and where the factory location is) and it worked out great.
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Paul
2007 Four Winns Horizon 220Mercruiser 350 Mag MPI w/ Bravo III Drive
2004 Ford Explorer Limited (V8-AWD)
Pomme de Terre Lake (Southwest Missouri)