No worry about fakes, the mobiles are so cheap it's not worth faking them. The only pitfall is 2nd hand mobiles. Thais drop them often so buying 2nd hand is stupid. The cheapest basic Nokia model cost about 950THB, these are not locked so you can use them back home no probs.
No need to worry where you buy one, just look in the shops at MBK or Panthip or Tuk Com or a zillion other places around Thailand.