I think that we forget how much even we adults have to train ourselves to have the vocabulary and stamina to read meaty books. And we also tend to discount the satisfaction gained from reading something with a little challenge to it rather than something that was sweet and tasty but ultimately unfufilling.
The more you read books that push you, the better you become at reading them. You assimilate the vocabulary, the literary allusions, the style of using compound complex sentences rather than simple sentences and short dialogue. For example, I've read some of Jane Austen's books several times each. I just read Northanger Abbey for the first time about two weeks ago and I breezed through it, laughing all the way.
Similarly, I tried to read Master and Commander over a decade ago. While I could appreciate that the writing was finely crafted, I had trouble following the story. Last year I gave it another try. Looks like ten years of reading Austen, Dorothy Sayers and other harder books had given me the scaffold I needed to enjoy the O'Brian.
There are lots of ways to feed your inner reader. The Well-Educated Mind by Susan Wise Bauer is a nice place to start. I has a section on how to read a book and then a listing of recommended classics, with some overview and probing questions to help you think through the story.
Another thought is to grab one of the great books lists and just start reading. Start with what you can handle or that is a mild stretch and just keep building.
Another idea is to use a list designed for classical homeschooling like Ambleside Online. Designed for kids, but there's no reason that you can't enjoy the same selections too. I read about a homeschool mom who was using AO for self education and thought that this was a brilliant idea. Even if the early stories are some that you might have read before or that you can easily handle, they will help you form a basis for enjoying the jewels that are to come later.
You can even just walk through the fiction section of the library and grab a handful of classic books that you've heard of but never really read (except, maybe in an illustrated abridged version or comic book form). That was how I put together my Boys Good Books reading list. Browse through both the adult and the children's fiction. It is hard to predict where some titles might end up. And you don't want to miss something great either because it was just a children's book when initially published or because it's now been moved to the adult section because kid lit has gotten so watered down
Sure you've seen movie versions of Alice in Wonderland, but have you read the book? How much is Pirates of the Carribean riffing on Treasure Island? Did you know that Heidi has a theme of redemption and reconcilliation running through it? Did you catch the Lilliput allusion in Night at the Museum? Are you ready for the grand-daddy of all vampire stories - Dracula?
Don't wait for the best time. These are the rich stories that will help you to cope with the uncertainties of today. You really are capable enough for these books. Just read it.