Personally not a fan of the reboot movie trilogy. Decent generic sci-fi, but not really representative of what Star Trek is.
I think the best movies to get started on are probably the Genesis trilogy. Wrath of Khan, Search for Spock, Voyage Home. Afterwards, Undiscovered Country. That should cover the good Kirk movies, which is where I feel Star Trek really became what it was through the peak of its run. Movies 1 and 5 are more supplementary material for the die-hard fans, they are just not that good. 1 is a long-outdated visual effects showcase with poor pacing, and 5 is basically a Mary Sue fic directed by Kirk's actor.
Afterwards, I agree that TNG is a good choice. Due to its very episodic nature, it is very possible to just pick some highly-rated episodes to get going with instead of just watching it front-to-back. Might even be recommendable to watch a few fan favorites to get some good impressions. The first two seasons were by far the roughest, so starting out with that gives you something that is not really representative of what the show can be at its best.