I had a problem getting past the old cheesy 1960s sets when I was a new Trek fan. So I wouldn't recommend watching the Original Series (Remastered) unless you have an affinity for 1960s or classic television shows.
My Recommendation After Watching Star Trek 2009....
1. Star Trek lV: The Voyage Home (The Movie)
2. Star Trek Vl: The Undiscovered Country (The Movie)
3. Star Trek: First Contact (The Movie)
3. Deep Space Nine Season 3 Cliffhanger (episode title "Adversary")
4. Deep Space Nine Season's 4-7
5. Voyager pilot episode (episode title "Caretaker")
6. Voyager Season 3 Cliffhanger (episode title "Scorpion Part l")
7. Voyager Season's 4-7
Side Note 1:
Well, here are some trailers from the above list to give you an idea...
VOYAGE HOME TRAILER:
http://www.traileraddict.com/trailer/star-trek-iv-the-voyage-home/trailer
UNDISCOVERED COUNTRY TRAILER:
http://www.traileraddict.com/trailer/star-trek-vi-the-undiscovered-country/trailer
FIRST CONTACT TRAILER:
http://www.traileraddict.com/trailer/star-trek-first-contact/trailer
DEEP SPACE NINE TRAILER:
http://www.youtube.com/watch?v=L4kebBWQfCM
VOYAGER TRAILER:
http://www.youtube.com/watch?v=b1PX9E2RsgU
Side Note 2:
Oh, and I wouldn't recommend starting at the beginning of any of the Star Trek films either. Star Trek: The Motion Picture can be viewed as slow and boring if you are not used to Star Trek. And Wrath of Khan takes a good 20 minutes before it picks up. Plus, it helps to know what happened in the Original Series episode, too.
Also, I don't recommend watching Star Trek: Enterprise the TV Series until you have watched the other series in their entirety. Enterprise has had the weakest character development, acting, and unexplained story lines ever. It also had a knack for raising serious question as to it's canon (i.e. validity or believability next to the other Trek series).
As for the Next Generation: I would watch Seasons 3-7 to start.
So your viewing order should look like this for all of Star Trek....
1. Star Trek lV: The Voyage Home (The Movie)
2. Star Trek Vl: The Undiscovered Country (The Movie)
3. Star Trek: First Contact (The Movie)
3. Deep Space Nine Season 3 Cliffhanger (episode title "Adversary")
4. Deep Space Nine Season's 4-7
5. Voyager pilot episode (episode title "Caretaker")
6. Voyager Season 3 Cliffhanger (episode title "Scorpion Part l")
7. Voyager Season's 4-7
Then finish up your Trek viewing with....
1. Next Generation Season's 3-7
2. Next Generation Season's 1-2 (could watch after Season's 3-7)
3. Star Trek Movies 1-10 (Complete)
4. Star Trek Deep Space Nine Season's 1-3 (could watch after Season's 4-7)
5. Star Trek Voyager Season's 1-3 (could watch after Season's 4-7)
6. Star Trek: The Original Series Season's 1-3 (New Remastered Version) (Enhanced Special Effects, Picture, & Sound)
Bonus Series (That are not perfect but entertaining):
1. Star Trek: Enterprise Season's 1-4 (Complete)
2. Star Trek: The Animated Series (Complete)
Side Note 3:
Also. There is one more thing I would like to add: The best option in finding the episodes I mentioned (in the above list) when renting them from Netflix is to check out the detailed episode listing of each of the seasons. It is a feature you have to actively click on when checking out each of the TV series.
Anyways, I hope this was helpful.
Sincerely,
~LS.