Controlling a 4 channel amp for stereo

I want to use my deck and run it to a 4 channel amp to amp up my door and rear speakers. However, I am curious if having the amp up loud and turning the deck down to low will produce excess noise. I'd rather have the amp up high so I don't have to climb into the trunk if I want the volume really loud, but I don't want excess noise either. Is this a problem in anyone's setup? I plan on getting a power acoustik amp. Thanks!

What HU are us using? Stocker? Aftermarket?

Plus if you set the gains properly you should never have to "turn the amp up". Gains are set with the deck at max volume, then you set the gains to where the speakers begin to distort, then turn it down just below the distortion point.

I am probably getting some form of DVD player. My concern is if having the amp always cranked and sending an attenuated signal from the deck would be more likely to introduce noise from the amp.

The amp is never "always cranked". The only time the amp is working/cranking is when it has an input signal to amplify. For an amp to be cranked all the time it would have to be a Class A type amplifier. Car stereo amps, for the most part, are Class A/B amplifiers which are much more efficient than Class A amplifiers. Class A amplifiers are at full power all the time whether there is an input signal or not. If you have excessive noise with the volume turned all the way down you either have your amp's gain set too high or your amplifier has a very high noise floor.

I think you have it wrong. Class A means the signal is amplified straight out (no phase inversions). Class AB means the signal is split into positive and negative signals with a phase inverter then combined using a center tapped output transformer. Its got nothing to do with noise, just effeciency.

My concern is in fact the noise floor. I guess I'd want an amp with an option to control the volume remotely. I'll wire up my friends amp to my speakers and see if there is any white noise just from having the amp so loud.

I think it's you that has it wrong here. Class A, A/B, D, etc. describes how the circuit is desinged to operate. And unless you have a tube amplifier there is no output transformer. Solid state designs don't use output transformers.