My entire audio system is wired to the ACC/accessory lead to the battery and its fusible-link for maybe 50 to 80 Amps. All in all, the audio system won't draw any more than 15 Amps. But in your case, you would indeed want to wire it to the battery with the amp's own fuse. In that case, you would want a dashboard switch so it doesn't draw juice when you start the car. Put it another way -- all my audio components are separately fused and switched under the ACC circuit.
Also, someone else mentioned this: you'd probably want something like a truck battery of the "deep-cycle" kind, or a "deep-cycle" battery that fits your car.
I grew into adulthood during the Golden Age of rock concerts. I always found myself dancing with my girl mere yards from the bandstand or stage. Now, people say I need hearing aids, and I have tinnitus. It is refreshing to see -- in the 21st century -- someone who likes his music so loud that it will turn his ears and brain-cells inside out. It used to be the case that people like us would drive around with their windows open and their cars thump-thump-thumping to the beat, annoying every nearby driver at the stoplight. Now, people drive with their windows closed, and they have Blue-tooth ear-buds connected to their 21st century sound systems.
Truth be told -- I'm not sure what millennial 21st century music sounds like. After Eddie Van Halen died, I bought three Van Halen album downloads and the "Van Halen" CD. Few months ago, I bought my first Metallica album and proclaimed "Wow, man! This is all new shit, man!" Then I discovered the album was released 28 years ago.