I have to say that the low end Pioneer speakers are just that, low end. I still have my TS-A6903i (6x9 which i can see over in the corner) and my 10" TS-A2501i speakers are currently staring me right in the face. For some reason Pioneer only do really top end gear which is good, or bottom of the run gear which is ropey at best .. but nothing in between???
For low end amps, I do like Pioneer amps, although my friend said they're not what they used to be. I currently have and old school Pioneer amp running my Morel Tempo 6 speakers. The sound is warm and full ... basically, sounds like a cheaper version of my JL audio amps ... but for me, JL audio amps have the edge.
On your battery, it should be fine if your alternator is up to the job. I killed two Varta batteries in a matter of months, because my tiny alternator was only pushing out 30 amps. I've since had to upgrade my cars charging system and for convenience I picked up a huge Varta battery from a car breakers yard, already charged for less than a 1/4 of the price of a newer, lower powered Varta battery .... result!!
However my advice is, ditch the sub/speaker set up ... especially the speakers, keep the Pioneer amps, but look to DLS for speakers, by far and away the best speakers I've heard under $100, and try for a JL Audio Sub of some sort. Like I said, the low end Pioneer gear is pretty ropey, I've owned enough of the stuff to know that!
http://www.avmover.com/classifieds/editors-choice-best-100-car-audio-speakers-dls-performance-speakers/
last point, a cap is going to be the least effective part of any audio system!
http://www.avmover.com/classifieds/power-caps-most-recommended-but-least-effective/ - Watch this :)
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if the headlights are dimming and you wanna sell a cap to fix it, why are we putting on the amp? We should be putting on the headlights because that’s what you’re actually having a problems with
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All the best :)