This may seem like an odd recommendation, but for beginners I actually recommend watching popular Japanese TV dramas with subtitles. This is based purely on my own personal experience over the years. You may not understand many of the spoken words at all, but the episodes tend to be very entertaining (which is important) and you subtly learn the rhythms, patterns, and manner of speech for Japanese people, which is actually quite helpful beyond just understanding vocabulary.
This created a huge turning point for my ability to understand Japanese speech. After watching these (very entertaining) shows for a while, my ability to parse Japanese speech increased dramatically. To give an example, native Japanese speech used to be an incoherent jumble of sounds in spite of my studies. After spending time watching these shows, I suddenly started being able to understand the structure of spoken sentences, which means I could start picking out words and phrases, even if I didn’t understand what they actually meant.
I haven’t really tried watching anime so much. We do have some children’s anime movies, but I personally recommend drama series over anime because there is something about observing (semi-)real human interaction that aids in the learning process. Perhaps it’s some innate thing. For what it’s worth (and I may be dating myself), two of my favorite series were Hana Yori Dango and Gokusen. You should be able to find these and other good ones on YouTube these days.