In the series' first book, "Harry Potter and the Sorcerer's Stone," Harry received a broomstick after the head of Gryffindor house witnessed his natural quidditch talent. This first broom was a Nimbus Two Thousand, which was the newest model available at that point. He used this broom throughout the first and second books, but during a quidditch match early in "Harry Potter and the Prisoner of Azkaban," an encounter with dementors caused Harry to fall from his broomstick, which flew into the whomping willow tree and was pulverized.
After Harry's Nimbus Two Thousand met its untimely end, he was forced to use a school-provided broom while he decided on a new broom to purchase for himself. This broom was a Shooting Star, which, according to J. K. Rowling's "Quidditch Through The Ages," was a slow and cheap broom that worsened in quality as it aged and hadn't been produced since 1978.
Later in "Harry Potter and the Prisoner of Azkaban," Harry received an anonymous Christmas gift: a Firebolt. The Firebolt was introduced as a brand new model in this book, one that Harry and all his friends coveted, but couldn't imagine affording. Harry used the broom, which turns out to be a gift from his godfather, Sirius Black, throughout the rest of the series. No newer models were introduced after this book.
In "Harry Potter and the Chamber of Secrets," the second book in the series, Harry's nemesis, Draco Malfoy, buys his way onto the Slytherin house's quidditch team when his father purchases brand new Nimbus Two Thousand and One broomsticks for Draco and all his teammates. This was a point of great tension, as Harry's teammates counted on Harry and his superior broomstick for victory. Harry's other friends who owned broomsticks purchased theirs from the Cleansweep or Comet series of brooms, which weren't as expensive as the Nimbus series, but weren't as poor in quality as the Shooting Star.