Hi John! A couple of questions for you so somebody can better help you out:
1). Are you using the international version or the US version of the S3? (The universal version has a significantly better DAC inside).
2). What headphones or IEMs are you using with your S3?
3). What are you trying to change/improve about your musical experience? More/less/different bass/treble/midrange/impact/soundstage/je ne sais quoi? (It may also help if you list some of your musical preferences here as well).
As an off-the-cuff recommendation, I have the US version of the S3 and don't really see much point in an external amp without a DAC as well. Conversely, I see using a DAC/amp combo with the S3 to be a fairly enormous improvement in pretty much every way (depending on the DAC/amp used, of course). I got an Apex Glacier and Meier Audio PCSTEP in yesterday, and they most definitely improve the performance several orders of magnitude over the stock headphone jack. (Although, to be fair, I'm not a fan of the sound out of the jack by itself... at
all).
Hopefully this will help you find more help! You might also want to check out the frequently-updated thread on Android devices and USB DACs
here.
And if nobody's given you the traditional Head-Fi Howdy yet, let me be the first:
Welcome to Head-Fi!!! Sorry about your wallet