I'd go with 32GB personally, but that's because on my iPhone (I know I know...) apps alone take up 16GB+ and I went with a dark phone, because using the phone in the dark becomes so much better due to the device taking a backseat. (especially when watching videos in your bed or what have you)
All this is because I'm a media guy and need the storage... or want it.
I'm sure 16GB can get you by relatively okay though if you've been living on 8GB, keep in mind though, if you take videos and photos you'll adore the extra space, especially as videos on the GS3 are 1080p.
The S3 has a SD slot, so if you don't need even those 16 extra GBs, I'd go with the 16GB model and top it off with a nice fast 32GB SD card, 16 if you're "cheap"
Glassed Silver:mac