The Enterprise was the first Earth-built starship to mount a warp drive capable of achieving Warp 5, although even that was mostly a theoretical limit.
When the ship left port, it was armed only with torpedoes of unspecified yield and low-power pulse weapons of unspecified type; both proved to be rather feeble compared to the weapons carried by the ships of other space-faring races at the time. The crew were able to install three phase cannons without returning to Earth for a refit, substantially improving the ship's combat capability. The ship's original torpedoes were eventually replaced with photonic torpedoes during a refit at Earth.
The Enterprise was the first Earth ship to mount a transporter system, but the device was not generally trusted and only used to transport living people as a last resort.
Notable Crew Members
Complete Lack of Lineage to Other Trek Ships
Despite there being on-screen evidence for spherical type starships shown throughout the earlier Trek shows; NX-01, looks like an Akira-class starship, albeit made a bit less fancy.