I think the 20th century will be especially well-represented, not just because of the huge list of figures and events, but because the advent of record-able media via radio, film, and finally the Internet arrived then, which allows for a lot more preservation.
Authors...hmm...
I think Jane Austen and the Brontes will survive well enough. There will always be a market and desire for those sorts of romance stories, and theirs are among the best-known and beloved in the West, and get the added boost of being written by women and thus can be taught as crucial parts in the feminist tradition as well.
I'd like to think Dickens will survive as well...after Shakespeare, he's arguably the biggest figure in British literature. Victor Hugo, Fyodor Dostoevsky and Leo Tolstoy have good chances among 19th century writers as well.
A vital characteristic is that old problematic phrase "universality," I think. We don't live in Greece or Sumeria, but something in Homer and The Epic of Gilgamesh resonates today (ditto the Moses and Jesus stories, when viewed as literature.)
Love stories are pretty universal and timeless, so again, Austen and the Brontes, having cornered those, have a good chance...if I had to pick an American novel which might stand the test of 2000 years, I'd pick "The Great Gatsby" by Fitzgerald...a love story, and I think it tackles a pretty timeless theme, wanting what you cannot have, why and how you want that thing, trying to change yourself to attain it, how love and wealth are intertwined, etc. In a way, it and "Great Expectations" are like modern-day fairy tales wherein the getting of wealth is the incredible occurrence.
"Moby Dick" has plenty of arguably-universal themes as well, so that's another nod.
Discussions on the meaning of being will persist as long as we do, and Dostoevsky is a leader there, and could see Nietzsche lasting as well. Camus and Sartre provide a nice tag-team for existentialism as well.
The 1900s to 1950s produced so many great pieces of art, film, literature and music that I think that period will be well-represented.
Excluding Shakes (since he's too early to fit this time period) if I had to rank my other 5 favorite authors in terms of their likelihood of surviving that long (though I hope they all do, of course, and survive well) I would say:
1. Dostoevsky, for reasons given
2. T.S. Eliot, as he's arguably the best English language poet of that century (always helps to stand out that way) and his fixating on the past and previous traditions and myths could make him a pretty interesting figure...they'd be looking at mythic traditions through the prism of a writer who HIMSELF would be old enough to be nearly-mythical to them, in the way the Ancients are to us now.
3. Virginia Woolf, for her fantastic prose style, critically-acclaimed stories, and again, her place as a feminist writer could give her a boost over time and be taught in terms of her social as well as literary relevance.
4. George Bernard Shaw...already common knowledge of him has shrunk, as socialism/communism saw defeats in the 1980s and subsequent decade...that being said, he's a pretty prominent writer in that vein, the popularity of playwrights wax and wane, so he could make a comeback, especially if those economic policies did in later centuries, and "Pygmalion" is a classic of British/Irish Literature, and that alone might help his case--even if his other plays were forgotten, it'd take a lot of change for Anglo-American culture to forget Eliza Doolittle or Henry Higgins...it's 2000 years, so it might well happen, of course, but still, that's as good a shot as any he has.
5. D.H. Lawrence...I flip-flopped between Shaw and Lawrence here...but even though I think Lawrence's novels are fantastic and are rightly canonized in the Modernist and British tradition...2000 years from now...will we read them? There are universal themes dealt with in them, but not like in Austen, Dickens, or Dostoevsky. He's not the greatest poet of his language and time, like Eliot was. You couldn't argue for him as a social figure the way Woolf as a feminist might survive. And it's hard to imagine a social movement which could revive him the way a Leftist world might gravitate towards Shaw. He's still an amazing writer and I hope dearly that he'll survive, but if he does, it'll be on the basis of his great novels alone,--which admittedly isn't a bad way to go.