Оба варианта правильные.

Оба Ваших варианта правильные. Ещё можно сказать так: "это становится интересно"

Both examples u said were right, but one would sound better than other in a different context. And the main difference - the subject (scroll to the last paragraph, if u dont wanna get bored xD) "Это становится интересным" - In this case something (or someone) is becoming interesting by itself. Here u need a subject and the adjective´s got the exact ending. Example: Книга становится интересной - The book becomes interesting. So, the story is getting more exciting etc. ("Книга" is feminine, so the adjective gets the feminine ending (here its also Instrumental case) - "интереснОЙ". But its not that important now, we are talking about other stuff XD) "Становится интересно" - here u dont even need a subject. U are just talking about some situation. Example: Становится интересно читать эту книгу - It´s getting interesting to read this book. So, I become interested in the story. Someone´s starting argue or fight in the club and u say as a joke "woa, it´s getting interesting!" - "Становится интересно!" would sound better as for me. So, the conclusion is - "Становится интересно" is a better way to express the phrase "It´s getting interesting", when we dont have the exact context. Thanks for attention *bow* :D

Лучше всего говорить "я начал интересоваться (чем-то)" или "я заинтересовался (в чём-то)"