How long did it take for the Borg to reach the Alpha Quadrant? Was the entire journey made on transwarp? What was the relative speed metric of vessel sizes, speed e.g Transwarp, SlipStream and just Warp Drive?
The Borg made transwarp gates, at least one in the Alpha Quadrant and one in the Delta (more are highly likely) that were used to jump from one to the other.
Here’s a description of Borg transwarp conduits from the forum thread The Borg's Super Speed!:
A transwarp conduit, also known as a transwarp corridor, was an artificially-created energy conduit through a realm of subspace known as transwarp space. They were utilized by the Borg to cover great distances in a relatively short period of time. Accessed via tachyon pulses of alternating frequencies, the conduits contained a matter stream in which a vessel could reach velocities at least twenty times greater than the maximum warp speed of a Galaxy-class starship, in a process Lieutenant Commander Geordi La Forge described as "like falling into a fast-moving river and being swept away by the current." (TNG: "Descent", VOY: "Dark Frontier", "Shattered")
This allowed the Borg to deploy vessels almost anywhere in the galaxy within minutes, giving them a decisive tactical advantage
The speed of "normal" Transwarp is very limited. But after the assimilation of an species, who had another drive system called "quantum slipstream", both drive systems were integrated by the Borg and the new and improved Transwarp was incredibly faster.
The timeline is not exact as I do not recall the exact dates.
In Enterprise researchers in the artic uncover a small group of borg who were from the movie First Contact. They had come from the future to try to stop humanity from inventing warp drive technology thereby eliminating the federation from history. In the Enterprise episode they ended uo sending a signal to the delta quandrant. However little was taken of notice because the signal would take five hundred years to reach the borg. In fact, the episode when Q reveals the borg is when the signal had just been recieved. It did not take long for the borg to make trip at all really. The only reason it was such a long gap was becuase the signal was too slow for galactic transmissions.