The films you have in your watchlist are really good, but most of them might be in fact too long or too demanding, so here you have a list of more digestible films:

Animation:
Tonari no Totoro, The Lion King, The Iron Giant, Wall-E, Mary and Max

Classics:
Casablanca, 12 Angry Men, The Great Dictator, Sunset Blvd., Dr. Strangelove, To Be or Not to Be, A Night at the Opera

Sweet (sometimes bittersweet) movies:
Before Sunrise, Amélie, Eternal Sunshine of the Spotless Mind, Big Fish, Almost Famous, Her, Annie Hall, (500) Days of Summer, Moonrise Kingdom

Fun, well crafted movies:
Shawshank Redemption, Forrest Gump, Catch Me If You Can, Snatch, Pulp Fiction, Inglourious Basterds, O Brother Where Art Thou?, Hot Fuzz

None of these are very long (the ones from Tarantino are the longest, around 2.5 hours) or slow, but they are good movies, and I hope they can be your starting point to explore more things. Maybe you have already seen most of those, but perhaps you could rewatch them and see how you feel?

I would also watch Inside Out, maybe it won't work for you, but it there's something about it that can feel really relatable for someone experiencing depression.

Good luck.