Hey man! There are a bunch of places to look, but you've already found one of the two most important. Head-Fi tends to focus more on what headphones sound better from the S3, what external solutions one can use for it, what applications perform better, etc. XDA Developers is the other biggie, and they tend to dig into the software side of things, going as far as replacing the kernel of the operating system for another that is optimized for audio. As far as which specific threads, that depends more on what your specific question or area of interest is.
As an off-the-cuff recommendation, I'd say check out Neutron Media Player (if you haven't already), and if you don't have a pair of decent headphones, definitely look into that first. You can then look into an external DAC and/or amp (which is the point of this particular thread), which can also provide a large improvement in the quality of the sound you're getting.
Personally, if I had somebody with a budget around $200 looking for a starter system that should utterly decimate the audio quality of the S3 stock, I'd say Klipsch X10 and iBasso D-Zero. But that's based on MY preferences, which may have absolutely nothing to do with yours. And figuring out what brings you closer to the music is a big part of the fun of this whole endeavor
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Take a look around man, and if you need help, people are here for you. I would caution, however, against posting at XDA without doing a significant amount of searching for your answer first... Those guys are super knowledgeable, and they have a markedly low tolerance for questions they don't think they should have to re-answer. Just a heads-up!
And just to be the first to say it: Welcome to Head-Fi!! Sorry about your wallet
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