I'm a firm believer in open-gate fandom, so I say jump in any which way that feels right!

I'm a longtime Trekkie and even I don't get half the references. Its mostly just bonus gags slipped into the very fast dialogue in the show. Give it a shot!

You might also be interested in Strange New Worlds; it's a new series that, IMHO, does a great job of capturing the spirit of older Trek series.