My recommendations are:
Gone With the Wind
The Haunting of Hill House
Watership Down
One Flew Over the Cuckoo’s Nest
It doesn’t matter to me whether they are classics or not, I think they’re just darn good books. If they fit your criteria, I hope you will enjoy them as much as I did.
To take a very classic view of “The Classics”:
The Iliad and The Odyssey, by Homer. Best books ever.
Also, I’d suggest:
The Canterbury Tales, by Chaucer
Le Morte de Arthur, by Mallory,
The plays of Sophocles and other Greeks: Antigone, Oedipus rex, etc.
Shakespeare—all
There’s even a classic naughty book. 
The History of Tom Jones, a Foundling published in 1749. Has some pretty raunchy sex in there and very funny too.
But its a huge, huge book for anyone to ever finish. Not a good beginner book at all.
“The one with the Mormons” is A Study In Scarlet. The Adventures of Sherlock Holmes is a collection of short stories, including some of his best. If you haven’t read it, you definitely should.
Another vote for Mark Twain. For novels, start with **Tom Sawyer **and if you like it progress to Huck Finn.
Watership Down is a fantastic suggestion.
HP Lovecraft has his stable of distinctive adjectives, but it seems to me his sentence structure is pretty straightforward. Try **Pickman’s Model **and **The Shadow Over Innsmouth **and see if you like them.
As for Jane Austen, let me share my experience. I too struggled with the language. Her sentence structure would draw massive red marks from any modern English teacher. One sentence in Northanger Abbey is so tortured that the editor of the edition I read misinterpreted it! And yet, if you can keep at it, your brain will become calibrated to her use of language, and then you can happily experience the delicious snark and page-turning interpersonal tension that have made her famous. Despite that one terrible sentence, you might want to start with **Northanger **- it’s a relatively simple and silly story. Save Pride and Prejudice and **Persuasion **for later, when you can read Austen smoothly. They really are worth it.
About 7 years ago I realized I never read Alice’s Adventures in Wonderland and Through the Looking Glass as a kid, so I decided to read them. What took me by surprise was how un-bizarre they were. Going by how weird many of the movie versions are, I was expecting a very strange story. But I remember thinking to myself at the time that the movies must have added extra strangeness to the story to fill out the time.
I did enjoy them though.
I’d recommend The Memoirs of Sherlock Holmes and The Return of Sherlock Holmes, if you’ve read The Adventures of Sherlock Holmes.
For a modern classic, try Holes by Louis Sachar.
For Shakespeare, try Macbeth. It’s his shortest great tragedy, IIRC.
I really enjoyed Twain’s** Life on the Mississippi**. Dunno if it’s a “classic”.
for a modern classic I’d recommend A Separate Peace by John Knowles. beautifully written.
Animal Farm, To Kill a Mockingbird, Watership Down, Wind in the Willows - those are must reads.
I’ve never read through The Hobbit either, though I have read all of The Lord of the Rings over many, many times.
I predict The Book Thief will become a classic. At least I hope so.
Point of advice: If you choose anything that was translated from another language (Homer’s epics, the Canterbury Tales, Beowulf, etc.), make sure you get a good translation. I found The Iliad horribly tedious, contrived, and boring the first time I attempted to read it, because of the terrible translation I was reading, but later found it a great, exciting page-turner.
And one general piece of advice for reading classics: A lot of them start off slow, before getting to the good parts. I like to read them while I’m traveling, because not having anything else to do on the plane forces me to get past the slow parts.
Substitute **A Christmas Carol **for David Copperfield much shorter and much better. **Animal Farm **and **To Kill a Mockingbird **are perfect for short and easy to read classics.
I third Watership Down. It is just a really good, fast-paced read and a unique work. In case you don’t know, it is based on the idea that rabbits have really complex societies with all kinds of drama. There isn’t another book quite like it.
To the OP: it has substantial overlap with what’s already been suggested here, but if you haven’t done so already, you might want to look at this old thread:
Recommend a classic novel that’s also a page-turner?
I thought Frankenstein was great and an easy read. You can’t really go wrong with it. Another ‘fun’ classic is Candide by Voltaire.
One thing I’m glad I did was read the book of Genesis. I thought it was fascinating and beautiful in a way - besides being the source of so many stories and references. If you’re into some light reading. 
Last year, I fell in love with Parade’s End by Ford Madox Ford; doing online research, I found several “experts” who were talking out of their asses. Then I Googled an essay by Kenneth Rexroth that enlightened me considerably.
I don’t necessarily recommend Parade’s End for a “beginner”–but you could do worse than check out Kenneth Rexroth’s Classics Revisited. They are two slender volumes (out of print but findable) of brief essays on classics from the beginning of literature to the last century–explaining why he thinks they are worth reading. If in translation, he recommends the best versions; he translated a bunch of Asian verse himself.
A goodly sample of Rexroth’s essays are available here. Many of the books are available on Gutenberg. Just reading the essays will make you feel smarter–it worked for me!
I came to the thread to suggest these books by Wilkie Collins. I found them easy to read and engrossing.
Joey P, now that you’re set for your next 2 lifetimes you could start planning your third. Note: For wiki links like the ones below, I recommend against reading a wiki summary of a book, at least until you’ve finished the book, because wiki tends to give away too much of a plot.
Whatever a classic may be, if it was written in the past 35-40 years or so then I recommend the James Herriot (wiki) books about his life as a vet. They are collections of short, easy-to-read anecdotes that can be highly addictive – just one more anecdote and then to bed…well, just one more… You should be able to understand easily enough the few Yorkshire- and vet-specific words.
Martin Gardner (wiki) has an annotated edition of Alice’s Adventures. And it, like an annotated edition of Sherlock Holmes or whatever, can enjoyably increase a text’s readablity.
I also recommend Ethan Frome by Edith Wharton (gutenberg texts, wiki). It’s short, maybe like a novella, and for me at least it was a page-turner.
Could I also recommend another page-turner? Rebecca by Daphne du Maurier (wiki). The movie was, for me, at best a Classics Illustrated version of the novel that, due to (effectively) US mainstream movie censorship, changed a couple of important plot points.
When you’re in your 4th life, and after reading the first 56+ posts above, please post again with an update.
Good God, don’t read the Communist Manifesto. It’s the culmination of Marx’s work, where he assumes that you already know and agree with his economic reasoning. It’s a giant list of really radical ideas, many of them social instead of economic, poorly reasoned, and dull. If you want to get a feel for Marx, try Wage Labor and Capital. It’s no more than forty pages, so I’d be surprised if you couldn’t go through it in an evening. It’s worth reading whether you agree with him or not; it’s been pretty influential through world history.
I tried Sparknotes for Dracula since they’re free on the internet and the problem I had was that they had no problem spoiling things. It seemed to be designed to be read after reading the book. For example, I mentioned earlier that I tend to get characters confused so when I saw that it had the major characters listed I figured that would be a good place to start. Might as well take a look at that to get a feel for who’s who and which characters are the minor ones that I don’t need to pay as much attention to…right? So I’m glancing at it and right there in the description it told me who Dracula’s first victim was going to be and that they were going to die early in the book. I did just read the SparkNotes today, now that I’m done. I’m also planning to watch the movie tonight (the Bela Lagosi version).
Yes, that’s it, I knew Adventures didn’t sound right.
So, I’m going to load up:
Adventures of Sherlock Holmes
Hound of Baskervilles
Marvelous Land of Oz (actually, I already have that one)
Heart of Darkness
And Then There Were None
Murder on the Orient Express
I think I’m going to start with either Murder on the Orient Express or Adventures or maybe I’ll do one Adventure and then Murder, or maybe I’ll start with Heart Of Darkness… I still haven’t decided.
Also, for those of you recommending project Gutenberg, not all, but most of the public domain stuff is free on Amazon. Adventures of Sherlock Holmes, I had to get from PG but it would have only been 99¢ on Amazon. BTW, can I just plug it into the USB port and move the .mobi file over like it’s a jump drive or do I need to get Calibre?
Two more things. Now that the Kindle has page numbers for most books, is there a way to access the Table of Contents? I like knowing how many pages are left in the chapter. I hate finding a good spot to put the book down and then the next day finding out that the chapter ended two pages later. It would be nice if I could go to the TOC and see that the chapter ends on, say Page 164 and plan my reading around that. And with that, is there a way I can get the bottom to display the page number instead of the percentage without having to tap the top of the page?
Lastly, Delivereads was recommended here a while back. I signed up for it, but I have yet to see it updated. Is it defunct? Last I checked, the Delivereads guy is still active on his other projects, did this one fall by the wayside? I know I can get programs to send my own articles to my Kindle, but that’s not what I’m looking for.
Heart of Darkness is not what I would consider an easy read, to be honest. The others sound great.