Sometimes ㄱ sounds like "g" and sometimes like "k". Which one is right?

Both — the position decides. At the start of a word ㄱ is the unvoiced "k" of sky, with no puff of air. Between vowels it becomes a voiced "g" as in go. So 고기 (meat) is closer to "ko-gi" than "go-gi". Starting a word with a hard English "g" is the most common English-speaker habit in Korean and it is hard to undo later, so it is worth getting right early.