"I would like to thank everyone who chose me."
Translation:Beni tercih eden herkese teşekkür etmek istiyorum.
After thinking about this some more, saying tercih edenler is wrong here, I believe, because tercih eden is actually an adjective for herkes. So it's basically the "herkes" who "tercih eden" me :D.
So I guess I could say "beni tercih edenlere teşekkür etmek istiyorum", but that would mean "I want to thank those who chose me" rather than "I want to thank everyone who chose me".