I suggest watching Spirited Away, which I consider his best film. Although it evokes well-known fairy tales like Alice in Wonderland, for years debate raged about whether the whole thing is actually a metaphor for child prostitution. I thought this was the case, and Miyazaki eventually confirmed it (ie the "bath house" thing is a parallel to when children are sold to brothels, when a family can't feed all their offspring, or are in debt, etc).

I would also recommend Ponyo, Princess Mononoke, and Howl's Moving Castle. I reckon you might prefer those to the titles you mentioned.

On a non-Miyazaki anime note, I highly recommend Your Name, which is breathtaking (a romantic body swap tale that takes some inventive and bizarre metaphysical left turns), and especially Grave of the Fireflies. The latter is one of the most upsetting and stunningly powerful anti-war films I've ever seen; resolutely apolitical, about the effect of war on innocent children. It had me in pieces by the end. I really can't recommend it enough.