In the original Next Generation series the version of
ship is the Enterprise D. However by the time of the movie
"First Contact" the version of ship is Enterprise
E.
Enterprise C also made an appearance when it was transported
into the future and caused a temporal loop destroying the
Enterprise-D in the episode "Cause and Effect."
Zefram Cochrane was the first person to say "to boldly
go where no man has gone before," which was repeated
by Henry Archer and Jonathon Archer.
The first encounter for the audience with the Borg happened
in the Next Generation, when Q flung the Enterprise across
the galaxy.
Although some scientists in the 22nd century were the
first humans to encounter the Borg.
The only race that could damage the Borg was species 8472,
featured in Voyager. There were also the only species the
Borg have been unable to assimilate (until Voyager gave them
a helping hand).
Starfleet galaxy class ships include: Enterprise, Fearless,
Carolina.
Enterprise D has 42 decks and can transport over 6000
troops (alt. version).