I'm an American learning Mandarin so I'm not an expert but here are the first shows and movies I've been getting into as I begin to understand more.
The only show I've watched so far is SpongeBob Squarepants in Mandarin: 海绵宝宝
I get this from torrents, but I don't have subtitles for it. Luckily I know the first 3 seasons by heart. It is also available on some streaming sites/apps such as bilibili.
For movies, I really enjoyed Love Never Ends (2023) which has dual subtitles, both English and Mandarin which both appear at the same time and helps a lot. This movie has great production value, it's quirky, and is a little artsy. I watched it on an international flight, it was in the "art house" category, although it is also a drama, romance, family movie. It's kind of about a punk dude that has grown up and is trying to do his thing while aging within Chinese culture, so it teaches about culture as well.
Chunking Express (1994) is a comedy drama with fantastic reviews, but I haven't watched it yet. The trailer looked cool and I'll watch soon.
Only the River Flows (2023) was also on the international flight and was cool, it is a crime drama with good reviews.
Green Snake (1993) is an action fantasy movie that is a classic from the 90s. I'm trying to watch some 90s films so I can relate to Chinese people my age lol.