Your stipulation of "average wealth" is a little vague. After all, a person of "average wealth" in England would probably still have been an agricultural laborer or a factory worker. Since you ask about Great Expectations, though, I'll bump "you" up a little and say that you're a young man (sorry for the assumption, but most of the literature I've found focuses on men) trying to work your way up in society. You've been educated at a small school, you keep a modest apartment with a single servant, and you work perhaps as a clerk or a bookkeeper. Perhaps you're a court reporter, as Dickens himself was before he had his success as a novelist. Also, by "books," I'll assume you mean novels (since you mention literature).

The mid-1800's is a wonderful time to read novels. Thackeray, Dickens, the Brontes, Kingsley, Collins, Bulwer-Lytton, and many other writers are publishing. Though it's not always profitable, novel-writing is becoming a legitimate career choice for more than those who have other sources of financial upkeep.

Novel-reading is enjoyable for you, and it could well make up a good amount of your daily entertainment. It wasn't uncommon for families to sit and read together in the evening. As rail travel became more common, 'railway novels' were sold in or near train stations, cheap books to occupy your time while you rode from place to place. Novels are fairly affordable, and there is also a healthy culture of loaning books you've read to your friends, or of visiting your friends to borrow books from them. You might get your books from a bookstore or a book vendor on the street (the kind Oliver is accused of stealing from in Oliver Twist). You might also subscribe to a periodical which publishes novels serially.

The general attitude towards books is also changing in your time period, though there is still something of a stigma attached to them. Books, with their focus on emotion and scandal, have been attacked as immoral. Young ladies of a certain class are still told not to read novels, lest they sully their virtue. On the other hand, some books have achieved what we today would call cult status. Sir Walter Scott's novels were immensely popular at this time. The writers I listed before have also achieved great success. Charles Dickens is a celebrity and draws crowds to his dramatic readings--you might even go to one, for a small fee, the way we go to movies now.

Speaking of Charles Dickens, he played a significant role in helping to shape the image of the gentleman novelist (thereby making novels socially acceptable). He himself had a vested interest in making the novelist seem like a gentleman: his father had been thrown in prison for debt, leaving young Charles to work in a shoe-blacking factory. Having labored for pay was a blight on his class aspirations, and he kept this a secret all his life--he told his biographer, but swore him to only reveal the fact after his (Dickens's) death. For Dickens, being a novelist was more respectable (a key phrase in the Victorian psyche) than a painter, because a painter has to sell his or her own work in galleries, while a novelist simply responds to the demands of a publisher. Asking for money ("putting one's hand out") was not respectable. But that's a tangent.

To get back to your question, if you're richer (say, a member of the gentry), you obviously have greater access to buying books, but your interest in them might be lower. Novels are written, for the most part, by the middle class for the middle class. When you read, you read to educate yourself, to check the latest news and gossip, or to learn poetry. Some aristocrats were mocked for being semi-literate. On the other hand, even those of high station read novels (the Prince Regent of the previous era was famously fond of them), and novelists might be invited to dine with aristocrats in order to liven up the conversation--though, as occurred with Charles Dickens at least once, they might shock the higher-ups by using common vernacular or speaking about taboo subjects. (He exclaimed "Oh, lor', no!", and "It did not pass unnoticed" - from Newsome's Victorian World Picture -- it also mentions that Anthony Trollope was noted as being "rather loud and boisterous" at one party. It was not a compliment.)

On the other hand, if you're less wealthy (say, a factory worker in a city), you might still get your books through lending libraries. For a small fee, you have access to the latest volumes of novels, which were largely published serially. You would be following the story volume to volume much as we follow TV serials today, so you and your fellow novel-enthusiasts would flock to the lending library to get at the limited number of copies when the latest volume came out. There are stories of crowds in America meeting English ships and shouting for news about their favorite characters.

As a laborer, you might also not be particularly interested in these novels of manners and social mobility. You might want Gothic stories about ghosts and murders, or crime stories. In this case, you would be buying "penny dreadfuls," cheap and mass-produced books, often written rapid-fire by writers working under pen names (pen names that were sometimes shared by several real-life people, for the sake of capitalizing on one name's popularity).

I hope that helps satisfy your curiosity, at least partially. For further reading:

Newsome, David. The Victorian World Picture: Perceptions and Introspections in an Age of Change.
Tomlinson, T. B. The English Middle-Class Novel
Whelan, Lara Baker. Class, Culture, and Suburban Anxieties in the Victorian Era