I grew up with The Original Series, so I hope you enjoy your run-through! I would go with the remastered versions myself, even growing up with the old FX, just because it makes it more watchable to me, and to people I want to share the show with. It's easy to make fun of Mr. Shatner's acting mannerisms, but I think they're overly exaggerated for comedic effect. There's just something in the subtle interplay between Kirk, Spock, McCoy and the others that you really do get the feeling they've been a crew for a while, but that this Kirk earned his place with years of experience, and getting very lucky at times, in his words "cheating my way out of death and patting myself on the back for my ingenuity." Spock's death in the original movies was heavy, meaningful, and it really hit you that this was a big thing for Kirk. In the Abrams-verse, I don't get that it's very deep or meaningful with Spock to Kirk, nor do I get that his version of Kirk really deserves the flagship of the fleet directly out of the academy. I definitely enjoyed the updated FX (in ST 3 and 4, I could see the mattes outlining the ships and it's really distracting to me), but not the updated ship itself (engineering is
a brewery, and it's painfully distracting to me, there's a dangerous core with dangerous walkways in the middle of the saucer for no reason, wasting space, the ship's proportions just look distorted to me, and the bridge has enough lens flares blazing in the crew's eyes to blind them). It's great it's gotten people interested in Trek again, but I just feel there's an emotional core to the original movies, particularly Star Trek 2, Star Trek 6, and a number of episodes, that just isn't there in the Abrams movies. These movies seem so fast-paced there's almost no time to let anything sink in or register emotionally. They feel hectic and rushed. That's just me.
Back to your original point, Balance of Terror, Mirror Mirror, Enterprise Incident, City on the Edge of Forever, and Ultimate Computer were always favorites of mine. Which ones have you discovered so far?