where did you buy the phone from?
when i got my first android phone from best buy, they transferred my contacts using their special "black box" for free.
so if you still have your iPhone up and running, just without service, see if where you got your S3 to do that.
as for battery life, usually it takes about 3-4 full charge/discharge cycles to bring it to its fullest.
if you are not lasting say 24 hours you have a run away process running and eating up all the juice.
for me, it was an app called MEDIA SERVER that kept the phone awake. unfortunately, for me, a complete reboot from factory defaults was the only way to kill this...