I'm not convinced that the stories enjoyed by previous generations will necessarily be seen in the same light by the current generation of young kids.

What seems to speak to contemporary kids are typically much faster moving stories with little exposition. Critical classics from days gone by often don't deliver this, similarly stuff like Famous Five.
As such, my suggestion is start with those recommendations of (at least relatively) contemporary authors.

Similarly, while I get the advantages of e-books, there's nothing like letting your kids just peruse the library for an hour or two. Libraries are also generally pretty good at providing recommendations, whether through lists (eg, 'if you liked x book, then why not try y...') or just through talking to a children's librarian, who are often highly knowledgeable.

I remember my English lecturer at teachers' college stressing the most important thing was to have kids reading, no matter what it was. I've got over my own dislike of comics as I see how much my kids love them, and they've been a good gateway drug to a wider range of book styles and to encourage reading generally (and that's what I stress with my kids - reading a range of styles and levels of difficulty).