There is a lot to say for reading them chronologically: You will understand the "insider jokes". Classics tend to refer to other classics, you will understand more and have a better reading experience, when you are able to understand those references. A description like: "She was his Sancho Pansa." Will only tell you something about the person, when you know your Don Quijote.
But I do advocate to read only those books you are interested in. Life is too short to turn a pleasure into a plague.
Then there is the Bible. Most storys told are told in the Bible. It is not as vital to know the Bible for reading the classics as it is to know it for understanding old paintings, however it is nice to know it.
There are a few books you'd like to know on your way for their influence on other authors. Have a look at the curriculum of a university for an overview.
One of the most influencial books ever and one I think is highly entertaining is
‘The Life and Opinions of Tristram Shandy, Gentleman’ by Laurence Sterne. You will find one of the finest copies ever made in our library. It was made by Patricia. The book itself has an interesting story, which you might like to read, if so, google it. It is said to have been the favourite book of Goethe and a couple of other very famous authors. Read it yourself and you'll know why.