1000w rms on stock alt

First do you have your BIG 3 Wiring done?, if not do so.. learn more about it here http://forum.sounddomain.com/ubb/ultimatebb.php?ubb=get_topic;f=5;t=007801  you can do the big three for less than $30 and an hour of your time

A deep cycle will really only help when your running your system with the car off, both of my cars have then just for the hell of it.. its not much more than a regualr battery

A HO Alternator would ideally be the best for your situation, but try the the first 2 and see if it makes any difference what so ever, it certainly wont harm anything

After using three deep cycle batteries ranging from the basic 120 minute reserve Diehard deep cycle to an interstate 1200 amp deep cycle endloader style battery, I have not been too happy with the results.  Secondly, the longest any deep cycle battery has lasted has been about two years. 

After thinking of trying something new, I bought I Optima red top and installed it in my trunk in June, 1997.  The same month I replaced my hood battery with a Champion 72 month battery.  In May of 2002 I tested both batteries again on a Sun Tune battery checker and the little printout told me a story I am not about to forget. 

The Champion had 35% capacity left whilst the Optima had 95% capacity left and that was after I charged each battery for 30 minutes prior to the test. 

     After owning a chevy product with the same alternator, I had to replace four of them during my ownership of the car.  Get a larger alternator, preferrably a 150 amp kit that can be purchased from Summit Performance.  This kit modifies your current alternator by replacing the bell housing, regulator, ball bearing, and rectifier diodes.  One of my friends found a modified one at the junk yard and that was the last alternator I ever bought before I sold the car.

  Presently two different cars later, I still have the same Optima Red top in my trunk and a yellow top under the hood.  Combined with a 125 amp  stock alternator and a 1 farad cap, my system can barely sustain 1000 watts. 

Though the red top would work better starting your car, since that is what it was designed for, and the yellow would be a more sufficient storage battery, and you have 125 stock alternator; you might wanna get it all checked out.

I'm running a standard starter battery, can't even remember the brand; a yellow top in trunk, 105 amp alternator(aftermarket but not the 180 amp it should have been.) I installed a volt gauge to watch my electrical just in case, no dimming short of idle. I've got 1300wRMS and I play it at like 50/80 volume consistently which is pretty f'ing loud. I have no problems, at all.

I'd have the electrical looked at if you can't hold up 1000w.... Esp if that isn't RMS. :)

Upgrade the wiring in the hood. If still a problem, upgrade alternator. I really doubt it should be a problem though.