While I've never been much of a poetry aficionado, the life stories of these classic poets are almost all as fascinating as stink.
Alexander Pope (21 May 1688 - 21 May 1744)
As far as being a successful writer goes, Pope was born to all kinds of disadvantage. His father was a cloth merchant in London; although the family was certainly not poor, Pope was always ashamed of his family's lack of gentility -- reports differ as to his father's status, with some saying he was merely a salesman.
In an England of extreme anti-Catholic sentiment, both Pope's parents were Catholic -- this meant substandard schooling for the most part. Pope was taught to read by an aunt, and given lessons in both Greek and Latin by Taverner, a Romish priest. Catholic schools were allowed to exist in some places; At Twyford, where he wrote his first vicious satire, about the school master, he was summarily "whipped and ill-used", and thus only lasted a year. Around 1700, when Pope was still a pre-teen, a statute forbade Catholics from living in or near London or Westminster. The Popes moved to Binfield in Berkshire, from whence Pope became self-taught.
As well, he suffered from health problems, including a form of TB that deformed his spine and made him a physical pariah as well. He never exceeded 1.4 m (about 4'6"), nor did he ever marry. He was wracked with migraines for most of his life.
Despite his youth, he was introduced to the London literary set around 1704 by William Wycherley, a well-connected but only somewhat successful poet of the day. His first public accolades stemmed from Pastorals, published in 1709. In 1711, An Essay on Criticism brought him a lot of attention, and The Rape of the Lock, his most popular and enduring work, was published the following year.
He was exceedingly nasty in his work, and along with Jonathan Swift was considered to be the primary critical eye of his time. Pope regularly slammed people publicly, as often naming them explicitly as using pseudonyms. The most interesting work in my opinion was 1728's The Dunciad, a piece written as a what he called a "satire on Dulness", that very powerfully blasted many popular writers. He extended his metaphor -- of dull conversation, writing and thought at battle with reason and intelligence -- into a parody of the Aenid (which itself is the Latin answer to the Greek Odyssey).
Like in those classical epics, a great contest is held to find the greatest hero -- in this case, the writer who can urinate most powerfully. Eliza Haywood, who enjoys a resurgence of respect today, but was considered by "real" writers to be pedestrian at best, is offered as a prize: The winner will receive Eliza ". . . a Juno of majestic size / With cow-like-udders, and with ox-like eyes" (II 155-6). Some have suggested her treatment by Pope led to a reduction in her creative output; still others have postulated his rough hand was inspired by a crush of sorts. Either way, he seems a petty little man to me. Full portents of The Dunciad
Pope's fame was secured by his translations of The Odyssey and The Iliad -- he was reportedly the first British poet able to survive on royalties alone (with no prince or earl necessary to keep, sponsor or employ him).
In about 1713, Pope formed the Scriblerus Club with Swift, John Gay, John Arbuthnot and Thomas Parnell. I'd like to read more about them -- they sound like an interesting bunch, sort of a precursor to Dorothy Parker's Vicious Circle. They wrote a piece or two under the collaborative pseudonym Martinus Scriblerus.
Pope lived and worked in Twickenham for the last 27 years of his life. He continued to publish until his death in 1744; he died on his 56th birthday.