I’m thinking a three point hat, eye patch, hook hand, peg leg, and a parrot as a companion. Was there a famous pirate (or possibly pirates) that embodied all of these attributes, or were these amalgamated from different historical figures? Or were these maybe combined into a caricature though fiction writing or some other pop culture source?
The first chapter of David Cordingly's Under the Black Flag deals with myth and reality regarding modern conceptions of pirates. According to him, our visual of what a pirate from the "Golden Age of Piracy" (1650-1730) was inspired by the actual pirates themselves and is somewhat accurate. One of the pirates' frequent targets were ships carrying colorful fabric. Pirates often wore brightly colored scarfs tied around their heads. Pirates were also fond taking wildlife from the Caribbean, Central America, and South America so our image of pirates with parrots and monkeys also has a basis in reality. Pirates would keep these animals as pets and take them to England and British North America to sell. Because their business naturally involved combat they were well armed with pistols and blades as they are depicted in movies, television, and popular fiction. This also leads to the popular image of pirates with peg legs and hooks. The life of a pirate was incredibly violent and dangerous. Therefore, many pirates were injured in battle and bore lasting reminders of their battles. Eyepatches, wooden legs, and prosthetic hands were not uncommon.
The historical figure who shaped our image of a pirate more than any other is probably Edward Teach aka Blackbeard. In 1724 Capt. Charles Johnson published A General History of the Robberies and Murders of the Most Notorious Pyrates. This book was incredibly popular in its time and had directly or indirectly influenced pirate media since its publication. The most famous part of the book is its section on Blackbeard's short yet eventful career. Johnson's description of the incredibly tall pirate with flames in his long black hair created an image in the popular imagination that still lasts today. Johnson's book inspired many 18th and 19th popular works of fiction and nonfiction in print and on stage.
Blackbeard is the most famous historical pirate but the individual who had the most impact on our modern conception of a pirate is not a real figure at all. It is none other than Long John Silver from Robert Louis Stevenson's Treasure Island. The novel was originally published in a children's magazine from 1881-1882 and a single volume version was released in 1883. The story was immediately popular. Cordingly speculates that Johnson's brief description of a foul mouthed, unshaven, one-legged pirate inspired Stevenson. Stevenson himself claims that Silver was inspired by his friend W.E. Henley, an avuncular editor with a large personality who had a foot amputated when he was a child. Regardless of the direct source of inspiration, Treasure Island developed the blueprint for pirate adventure stories that even the special effects laden Disney Pirates of the Caribbean films follow. Stevenson built his book on previous historical and fictional texts work but it is Treasure Island that forever associated pirates with parrots, peg legs, maps, pieces of eight, and tropical islands.
Pirate speech, "arrrgh" "Shiver me timbers!" and the like, has a more recent origin. In 1950, Disney made its debut into live action features with an adaption of Treasure Island with Robert Newton as Long John Silver. Newton was raised in Dorset in Southwest England. The famous "pirate accent" that is instantly recognizable to 21st century audiences is an exaggerated form of a West Counties accent.
Sources: Cordingly, David. Under the Black Flag: The Romance and the Reality of Life Among the Pirates