Is your S3 unlocked to any network?
No: Not much point in doing anything with it in Turkey except using wi-fi which most bars have.
Yes: You can get a micro sim from Turkcell, Avea or Vodafone. All will do a package for a month to include texts & calls back to the UK, best you ask in all 3 to get the package that suits you.
No need for residency, just show your passport.
BUT
You may find that your phone gets locked, either when you are in Turkey or when you get home (as happened to my S3). If so simply go & get it unlocked again.
My advice would be to buy a cheap phone for 50tl then buy the right package of texts/calls you need & use your S3 for the internet via wi-fi.
Personal recommendation is to go & see Baris in the main Avea shop (along from the Fethiye market on the same side of the road towards the PTT), speaks very good English & extremely helpful, my sim was 49tl for the month.