I work in the car audio industry and I would say start with the big 3. It makes sense. What good is it to run 1/2/4 gauge power wire if you are only using 8/10 gauge ground? You are bottle-knecking your system.
Even after the big 3, you may still have dimming. Then, you should invest in a high-performance battery (Optima yellow top). Seems like you already did.
The next step would be a high output alternator. Some people prefer caps. Personally, I am not a big fan of them.

 

Being an Electrical Engineer and having worked in the car audio field for a few years I can say IMO caps are a very good thing to have and do help to lighten the load on your alternator and battery as well as helping your amps avoid power starvation. That being said, they are still no replacement for a good high-output alternator. You can only do so much with 110 amps before you just need more.

 

This is true that they CAN help, but make sure they are sufficiently sized. Not sure about now, but 1F caps used to be the largest size you could reasonably get, and thats just not enought juice to make any difference. 10-20F is more in the right range, but going to big will also be an issue as the response lag due to the charging will be slightly longer.

 

What size power wire is going to the rear of the car?

I would reccomend a real 4 gauge or 2 guage to the 1000/1 alone...

Upgrade the wire from the alternator to the battery to at least a real 4 guage, 2 - 0 is preferred. Also add grounds from the battery to the engine block, and to the frame of the car.

The cap is only a band aid... it WILL help with the dimming lights, but it also adds more load to your alternator as well...

If that doesn't work shoot for a Optima Red Top, Not Yellow!

good luck.