The basic form of "I" is 나 (informal, 저 is the formal form). 난 is the contracted form of 나는 = 나 + topic particle -는/은. You use it for talking about general things. 나는 18살이야. I am 18 years old. 나는 너를 좋아해. I like you. 나는 이제 자러 가. I'm going to sleep now. 내가 is 나 + subject particle -이/가. (This would normally give 나가 but it's an exception, 내가.) The difference with -는/은 is that -이/가 puts emphasis on the subject, so it's like "It's me who..." 내가 할게. I'll do it (myself). 내가 그랬어? Did I say that? 내가 먼저 갈게. I'll go first. In all these examples "I" is emphasized. 내 is the contracted form of 나의, which comes from 나 + 의 (possessive particle) so you can use either. It's just a matter of personal preference.