The Oxford Learner's Dictionaries are an excellent resource for English learners. https://www.oxfordlearnersdictionaries.com/definition/english/like_1?q=like like preposition meaning 5 - for example anti-utopian novels like ‘Animal Farm’ and ‘1984’

I don’t think it’s natural. In speech it would be more natural to say nothing and just pause. It also sounds bad to use “like” twice with different meanings close together. And neither “like” nor “such as” really make sense with “all kinds of movies”. You could say something like “especially”.