I think the most difficult thing about being a Starship captain is choosing which speed to use. One day it’s, “Chekov, warp factor two.” The next day, “Chekov, warp factor three.” Is there a galactic speed limit? Also, do they need to change the oil every few hundred parsecs? I never questioned these things when I was younger. Now I want to know.
I suspect that quantum effects ultimately obviate the need for lubrication, on the highly questionable basis that any two particles in contact with one another will also simultaneously be somewhere else, thereby reducing friction to nominal at best.
As for the speed limit, I consulted Memory Alpha:
Faster-than-light travel began after warp one, whereas lower fractional values were sometimes used to measure sublight speeds. Spacecraft ordinarily traveled at a higher integer warp factor.
By the 24th century, infinite velocity was designated as warp factor ten. It was considered to be unattainable by conventional means. Because of this, extremely high warp factors were indicated with fractional values between nine and ten, such as warp 9.975.
How about unconventional means?
In 2267, the Nomad probe improved efficiency in the antimatter input valve and energy release controls on the Enterprise, allowing the ship to achieve at least warp 11. When this happened, Montgomery Scott was in disbelief. Captain James T. Kirk ordered Nomad to reverse the modifications though, as the structure of the Enterprise was not designed to handle the stress of that much power output.
Then again, this was still the 23rd century; true warp ten and Duck Dodgers were still decades away.