Lt. Tom Paris was able to reach Warp 10 in a shuttlecraft in Season 2, Episode 15 "Threshold", therefore making that the fastest ship.
Depending on when and which source you use, The Enterprise, The Excelsior, Voyager, and even The Titan have all been called Starfleet's fastest ship. At one point in the books, the whole concept of Warp 10 being the highest warp speed available to a starship is explained away. It seems that warp speed is recalculated after a suitable technological event. So that what is Warp 10 increases like inflation or money over time.
Further the introduction of Transwarp and slipstream technologies have further made this question more complicated to answer.
Best Answer. In the third movie, as the Excelsior leaves starbase someone captain, engineer remarks that he looks forward to beating the speed records set by the Enterprise.
The Enterprise is always the fastest starfleet ship
If we are using only prime timeline it would be Voyager as they have done slipstream and transwarp that was initiated by them, unlike enterprise which seemingly used a conduit as they did not have a transwarp coil.
If we are considering other timelines. The finale of TNG, Beverly Picard's ship does Warp 13.
If neither of those situations are considered then Paris in the shuttle would definately be the top by actually hitting warp 10.
Tom Paris was just about everywhere when at warp 10 and overloaded the scanners with information.