Battery what cap do u recommend fro the jl audio 1000/1

First off, are you trying to stop lights from dimming? Because a capacitor is only a band aid to solving that issue. If you are using a capacitor for its intended purpose (to smooth out the voltage input to the amp, thus providing a more consistent voltage level), the general rule is 1 farad per 1000 watts rms. I hate to tell you caps aren't worth it, but this amp is a good amp. There are built in capacitors already. If you really want to see an improvement in your system, you will want a quality cap along side a quality amp. Look for an Alumapro capacitor. They go all the way up to 50 farads. High in price, very high in quality. Perfect compliment to an amp such as yours.