I tagged this as "youdont" to be a smartass, but the question deserves a more serious answer. I'm only a casual Trek fan (meaning I enjoy the movies and will watch TNG if I run into it while channel-surfing), but really, you may be overthinking the issue. Introducing someone to one of your passions is not more difficult just because the subject in question is Star Trek, anymore than it would if we were talking about, say, antiquing.
My wife has gotten me into antiquing/DIY/restoration basically by osmosis, just by watching her favorite HGTV/TLC shows while I'm hanging out in the family room. She never forced it beyond saying "I think you might like this show, wanna watch an ep?", the secret being that if I had refused, she wouldn't have pushed it. Now we regularly go shopping for vintage furniture/appliances to restore, which is fun merging of her design skills and my tech ones. Likewise, when I want her to check out something I enjoy, I will offer it up without expecting any more commitment than "sure, let's watch a bit and see how I like it".
So the movies would be your best bet. My personal favorite is First Contact, but you might be more successful with the Abrams reboot, which could provide an easy lead into the original films because of Nimoy's presence.
Just remember, if they aren't into it, let it go. Your passions remain just as enjoyable even if your friends and loved ones don't share them.