I'll second the Gorey and we started my niece on Lemony Snicket a little after two. That worked out well - at ten, her sense of humor is turning out nicely.
Also, the bargain bin books are terrific. When I get the chance, I raid junk stores and thrift shops for piles of cheap books. The niece and nephews love it - always plenty to read and no biggie if something is damaged or lost. Also, it's good to give them back to the thrift stores so they can sell them again. I usually shoot for books printed before the 1980s. That's about when advertisers started printing "books" to sell product and special interest groups started throttling things on their agendas, and that goes on both sides of the fence.
Be sure to pick up the classics, too. Aesop's Fables, Grimm's (sanitized or not, depending on your preferences), and the L. Frank Baum books proved very popular. There are several books in the Oz series and they're all good. Same with Lewis Carroll.
Also, expand your take beyond the lit. Pick up volumes of old encyclopedias, science books, text books, and especially old coffee table books. Those are almost always G rated and have great pictures. Even stuff like "Agricultural Survey of America" from 1968 will work - they'll like the pictures of tractors and cows and the exploded view of a combine.
I usually just skim for objectionable content and grab anything that looks interesting. You never know what the kids will pick up on, so throw a big variety at them.
And it's totally cool that you're reading and going through books already. That's absolutely the best thing to do with kids.
