What battery should I use to power a DIY boombox using car audio components?

I've been looking at car stereo boomboxes (DIY of course) and had a simple question on how to power the stereo: WHAT BATTERY SHOULD I USE? I plan on running a Kicker ZX300.1 mono amplifer to power three 4ohm SVC subwoofers (wired down to 1.53 ohms), and a wallmart headunit that I suspect draws around 10amps of power connected to Kicker DS60's. I'm also fairly certain that the amplifier draws 30 amps of power (300 watts / 10 = 30amps). If this is correct does that mean I need to have a battery / set of batteries rated at 40 Ah? (I know I need a minimum 12v to run car audio equipment, the question is based on the Amps Per Hour rating of the battery). I Guess what I am asking is does the power source need to be rated at the "x" Amps/Hour where "x" = the total amp draw of the system? Thanks!

No, Ah is to do with the total amount of ENERGY in your battery.

So, calculate the mean current into your equipment, decide how long it will realistically be on, with the engine off and then you can work out the battery life.

It is VERY unlikely you will be pulling 30 A continuously, you'll probably find its nearer 5 on average.

A 40Ah battery , on 30A, will last 40/30 Hours - just over an hour.

A 40Ah battery, on 5A will last 40/5 or 8 hours.