Most of the times I don’t LOOK for symbolism, it just sticks out. It usually happens when you know a lot about the context of the book, the period it was written in, the author’s system of thinking and, more than the message they were trying to convey, what kind of readers they addressed. Because one-sided symbolism is pointless, you need the reader to pick up on it.

So no, I don’t think you have to approach reading as a chore, since I assume it’s reading for your own pleasure, not for school. That being said, keep in mind that especially with non-current works you may need to have a decent base of general culture around the book, or read up on it. It’s not that hard and can actually be enjoyable. Also most classics would be orbiting Ancient Greek/Roman mythology and philosophy and the more religious would include the 2 testaments in their basic mythology and thought systems. The Romantics were quite interested in medieval myth and, maybe surprisingly, in the scientific advances of the day.

A little knowledge of literary movements can also be helpful, as they tended to turn their symbols into tropes - then the next movement would be a reaction to the previous one, so that might also help you understand more.

In any case, if all this seems overwhelming, there’s a lot of kind people on the www who explain even the more obscure writings, so I’d treat them as the great resource they are. To me personally it’s always a joy to find out new dimensions to a book I’m reading.