You can skip the NextGen movies after First Contact.  And really, that's the only NextGen flick worth watching (the reboot was in no small part due to those last flicks)-- there's some Nexus stuff I actually like (Picard vs Soran's whole attitude towards time and life), but really, you can jump from 6 to 8 no problem.  I don't even own the other flicks but those.  Just remember the movies, particularly the first one, are products of their time.

A couple years ago I watched the original series when it came out on Blu-Ray and I decided I would watch it in the mindset of someone who'd never seen the show, and that this show isn't connected to the movie or NextGenverse (cause really, it isn't).  And I enjoyed it on a whole other level, and the whole wild west aspect of it came out much more strongly, as well as the whole feeling of them being this one little ship at the edge of known space venturing out and encountering weird sh*t.

Remember, the die hard love for Trek came from all the series (well, not Enterprise... or really, Voyager either), not the movies.  And if you don't dig regular Trek, you might like Deep Space Nine, it's like the Fight Club of the Trek-verse, darker subject matter, big war arcs, religious issues in the forefront...