Please put API definition in the first priority. Please DO NOT build-in any 3rd party login system.
With API , every 3rd party login system is possible. Everyone can implement his/her FB/twitter login system.
I suggest define an OAuth-like authorization system.
English is not my native language. I try my best to express my thought precisely. I hope you understand what I mean. If any misunderstanding results from culture gaps, I apologize first.