Hmm… My particular advice would be to go on pleasure or interest. You could start with an anthology but it might make you feel like you are doing homework. Norton Anthologies are good though in that they give helpful biographical information and good notes. I think if you get an anthology, you should skip around until you see something that catches your eye, and then use that as your starting point— reading things in conversation with what you like. Or you could read it in order, which would surely be interesting, but more like homework!
Something to keep in mind is that a Norton anthology will probably have poetry or short stories, because including many novels it would make it extremely long.
I wrote out some recommendations. But first I’ll give some general advice that maybe be more useful (or not!) and then a comment on Shakespeare.
It seems one of your issues is that you get discouraged, because reading in a foreign language is slower and you could just read the translation. Another issue is getting distracted by other languages.
One way to approach these challenges is to read shorter works. For example, some famous writers on these lists wrote very long novels, especially in the 19th century. But some of these same writers also wrote shorter novels, novellas, short stories, poems and plays. You could choose a shorter novel or short story, or a novella. That way, you could get the satisfaction of finishing, and improve your language fluency at the same time. Of course, long novels have the advantage of getting lost in a world for longer, and the writers have a bigger canvas. But you can get distracted and not finish, which is discouraging. So it’s one solution.
Another tack is to read literary essays/nonfiction, which are some of the easier things to read. You could try some of the nonfiction on Brown’s list: Emerson’s essays, Frederick Douglass’s autobiographies, Thoreau (although the latter is harder IMO.)
Poems are harder. But on the other hand, you can get something from poetry in the original that you can’t in the translation, because it’s hard to translate the language’s music and meter, things like rhyme (internal and external), alliteration, plays with sound. So possibly it could be motivating to think you are getting something you can’t get by reading a translation. It depends on what motivates you though!
If you are interested in poetry, I like this podcast, Poem Talk, where they discuss different poems in detail. They have a lot of episodes on writers you might be interested in, including some on these lists: (a list of all the episodes is on the right): Art and power (PoemTalk #32) | Jacket2, a lot of more modern ones too.
Shakespeare seems like one of the hardest things you could choose. On the other hand, if it’s fun and interesting to you, that’s motivating in itself. When I was young and in high school, there were always several people extremely into Shakespeare (I also liked it.) That’s because the plots are compelling and dramatic, sometimes they are silly and obscene, they show great psychological insight, and the language is fun to say out loud, and often beautiful. You could try to memorize or to recite a speech or a sonnet out loud. We used to do that in school.
I would recommend a good edition with notes, maybe the Penguin or Oxford edition, because the language is quite different from modern English and the notes are useful for understanding it.
Personally, I would avoid the translations to “modern” English because you lose some beauty of the language. The “translations” would make it easier though. If you didn’t know, Shakespearan poetry is written in iambic pentameter. That means each line goes, da DUM da DUM da DUM da DUM da DUM . (An iamb is two syllables with the accent on the second one. There are 5 iambs in a line, thus pentameter— penta=5) In a “modern English” translation you might lose this rhythm, and you would probably lose it in translation as well. So it might motivate you to know that you could appreciate this aspect of the poetry and plays only in the original.
The book you linked could be useful for background info and to help orient you!
Another thing to keep in mind about Shakespeare is that the plays are generally divided into three categories— tragedies, comedies and histories.
I think the histories would need the most background info, as they deal with complicated lines of succession of the English monarchy (but your book would help.)
For comedies and tragedies, you could probably dive right in, if you had some notes helping you with the language. They don’t need as much historical background. For example, A Midsummer Night’s Dream takes place within a fantasy world, where people turn into animals, etc. Romeo and Juliet, Two Gentlemen of Verona and The Taming of the Shrew take place in Italy, but it’s kind of a fantasy Italy from the perspective of Shakespeare’s England, not a factual historical Italy. The Tempest also takes place in a kind of fairy/ mythical space (a main character, Prospero, is a magician, etc.) Thus, accurate historical information is not as important, although of course Shakespeare’s own situation shapes how he treats his subjects and some allusions of the language. Good notes would help you there though.
We often read tragedies like Macbeth and King Lear in high school and to be honest didn’t spend very much time on historical background at all. (Except we always talked about things like what theater was like in his time, etc.)
Again, they take work to understand, the language is far from today’s, so it won’t be easy beach reading. But it depends on you. I know people (native English speakers) who couldn’t read them at all and gave up. On the other hand, I also knew people in school (often young people) who got super into them and read many of them for fun.
Another thing to remember is that Shakespeare’s plays were written to be performed, not read. So you could watch some of the many adaptations.