Most movies, TV shows, anime, etc. will not be suitable for beginners. However, that doesn't mean you can't learn from them. At first, you'll just be picking out words here and there (as you mentioned above). Keep a dictionary next to you, pause often, and look up words (especially ones you keep hearing over and over). Don't get discouraged. As you gain more vocabulary and get comfortable with the grammar, your understanding will begin to gel.
Different types of programs have their own challenges. Media aimed at younger audiences tend to be easier to understand. Period films and sci-fi can be difficult. Watch out for dialects. For example, in "Your Name", Mitsuha and the other inhabitants of Itomori speak in a Gifu dialect, which won't be covered in a textbook.
One specific item I recommend is Japanese programming on Netflix, due to the fact that they have Japanese subtitles. You can pause it and switch between English and Japanese subtitles. Having trouble making out a word with listening alone? Switch over to Japanese and look up the word on the screen. At some point in your Japanese progression, get rid of the English subtitles, even if you aren't comfortable. (The English makes it harder to understand the Japanese.)
At the end of the day, language learning should be enjoyable and full of rewards as you open up to understanding new content. You can build up your base of knowledge (vocab, grammar, kanji) and also focus on what you find enjoyable in Japanese (news, anime, cinema, games, etc). And some time from now you can turn Your Name back on, kill those annoying English subtitles and experience it anew.
Gambatte kudasai!
