Yeah but they are kids. They might not get into it just cause its a classic.
Here's what I would suggest.
2 decent to amazing episodes of TOS; one especially where you have some great dialog with McCoy. Some mentioned would be perfect.
Pick the middle 3 TOS movies; Wrath of Khan, Search for Spock, and Voyage Home. Those are continuous, plus lend more to the dialog between someone impulsive and cowboyish like McCoy and someone calm and collected, like Spock.
After that, leave TOS. go straight to Encounter at Farpoint, and start them there so they not only can see time has passed, but provide continuity between TOS and TNG, as McCoy is in the pilot. From there, turn 'em loose on all TNG episodes EXCEPT Code of Honor. Roddenberry wanted that one, but it turned out to be a rather racist episode. no-one liked that episode.
Additionally, if you can find it, depending on the age of your kids, also include with this as a side, the episode "The Bionic Bunny" from Reading Rainbow. This is the episode where LeVar is doing the entire Reading Rainbow show from the set of TNG. I don't recommend this as a "behind the scenes" thing, but instead to tie some familiarity. No-one really knew the cast of TNG, except mainly LeVar, and Wheaton had just finished Stand By Me by the time the TNG pilot came out, and North and South was just in production, so no-one knew Frakes, as Patrick Swayze was getting all the attention in that miniseries.
With that, Season 2 gets them noticed thanks to Whoopi, and Season 3 explodes. If they aren't hooked by then, they never will.
BL.