Hayao Miyazaki is my favorite. I liked all the ones you mentioned, (Grave of the Fireflies is sad but well made)... plus others, like My Neighbor Totoro, Ponyo, Arrietty, Kiki's Delivery Service, Porco Rosso and Princess Mononoke. Last week, I watched From Up On Poppy Hill, which is not by Miyazaki himself, but his studio, Studio Ghibli. It is excellent.
I saw Slayers years ago, but will have to find out more about the others you mentioned. Did you watch The Melancholy of Haruhi Suzumiya? It was popular a few years ago.