Oooo - I'm a luver of puns.
A bit of electronics etc does help, but when not constantly involved, it's easy to get swayed by the hype. EG - caps have their pro's & cons, but for the most part, they are cons.
The only valid use I have seen in BIG audio systems for caps is to protect AGM batteries, and that comes from people with experience. But that also fits in what I have often said, namely that AGMs can supply big Amps (as in Amperes) - ie, usually twice the
short circuit current that an equivalent wet-cell can provide (because AGMs typically have half the internal resistance of a wet cell) - but AGMs do NOT like doing it. Hence caps to take the load off the AGM for short high-current bursts.
The only other situation is where a (second etc) battery cannot be installed close to the amps (amplifiers). But even then, a 12V 1.2AH battery is smaller than a 1F cap...
Many audio sites will also tell you that you get a higher PEAK SPL without caps. (That implies it might be higher still with wet cells rather than AGMs, but that might not be a valid conclusion.)
If your system was 100W, then voltage dips should not be a problem. That's around 10A and is equivalent to high beams.
The Fosgate P3001 is max 300W into 2 Ohms, hence about 30A input. Again, not much, and is probably be handled with most charging systems (alternators) unless lights and wipers are on etc. But it certainly requires good cabling etc.
And ANY vehicle usually benefits from
The Big 3 which should always be the first step for any performance electricals.
BTW - although Watts is strictly
ONLY an RMS value, there are other "rubbish" terms like Music Power (Watts) and peak power etc. Traditional "Music Power" IMO is ok because that was simple twice the RMS value (no doubt a marketers adaptation of certain electrical formula to make amps sound... er, appear more powerful on paper), but peak power has no application. Peak power could vary anywhere from Music power to 10x the RMS power.
The point being, you have to be careful what Watts they mean. Quality brands will only quote RMS because that is the only meaning for Watts, besides which it is the only meaningful application of Watts.
That Fosgate rating however is in Watts RMS. They quote a "peak" of 900W - whatever that may mean - but that can be ignored. (How long for? Is it a thermal rating, or max peak current demand rating, or...?)
But IMO you have come to the right place.
I am audio-naive and more into the electrical and power side of things - eg, batteries etc. But there are some terrific audio experts here that give (IMO) outstanding advice.
And others are gurus with alarms and remote start units etc.
Note that most are professional installers. (But not me, I'm just a a pest - amateur in status but possibly professional by application LOL.)
Anyhow, enjoy and welcome etc.
Any problems - just ask.
PS - I can like bling - especially in da'hoods etc, but I object when people think they have to have it. And if they can't afford it, and it adds minimal or no value anyhow...
I'd rather spend that
bling on an extra
cider beer, or a charity etc.