I'd suggest Middlemarch, Tenant of Wildfell Hall, and Beloved. No love for le Guin? If you're interested in Sci-Fi you should at least read The Left Hand of Darkness.

Personally, I wouldn't waste your time with The Stand and The Alchemist. If you must read King, I'd suggest one his books that are actually readable like The Shining or Different Seasons. I would pick Foundation over I, Robot for Asimov. It's a better book and more influential, I, Robot just has the name recognition from that Will Smith film.

Edit: When it comes to Hamlet. I strongly advise you don't just read it, you watch it. It wasn't written for you to read it was written for actors to perform to you. Watch a production first. Same goes for any Shakespeare or really any play for that matter.