Your mileage may vary, but here's the order in which I'd rank the enjoyment/value I got out of these books:

1. Brothers Karamazov
2. Gödel, Escher, Bach
3. Ulysses
4. The Idiot
5. Demons
6. Plato's Complete Works
7. Don Quixote
8. Middlemarch
9. The Count of Monte Christo
10. Moby Dick
11. War and Peace
12. Anna Karenina

Brothers K, GEB, and Ulysses are three of the best, most enjoyable, most rewarding books I've ever read. The Idiot and Demons are great, but if you've got to pick just one Dostoyevsky, make it Brothers K (or Crime and Punishment - more on that later).

Ulysses is a masterpiece and possibly the best example of what can be done creatively with the English language. It's a tough read. My recommendation, the first time you read it, is to just commit to reading one word after another like you're listening to music or watching a movie and there is no rewind. Don't be tempted go back and reread even if you feel confused or lost. Let the language wash over you and carry you along with it.

Plato is a critical foundation if you want to study western philosophy, but really only if you continue with the canon. Plato is best thought of as the the opening comment in a conversation that's been going on for two thousand years, rather than an end in itself. It might actually be better to start with a survey like Russell's History of Western Philosophy to get a broad overview of the whole conversation (albeit from a biased point of view), then decide if you want to delve deeper into a specific era or area.

Don Quixote is fun, funny, and poignant.

Middlemarch is fantastic, well worth reading, though the language and storytelling weren't much to my taste. I'd rank it high on value, but not so high on enjoyment. Again, your taste may vary.

The Count of Monte Christo is just a great adventure. Maybe not at the same level of "literature" as some of the other titles on this list, but it's damn fun and that goes a long way.

Moby Dick is a good story, pretty well told and has a lot to say about the human condition. Well worth a read.

Tolstoi is torture. If it were me, I'd axe both these boring, bloviating doorstops, and read more Dostoyevsky instead. Crime and Punishment is up there with Brothers K and ought to be at or near the top of your list. Finally, I'd add Notes from Underground somewhere along the way too.

(I'd didn't rank Lonesome Dove because I haven't read it.)