Probably a toss up between The Next Generation (TNG) and Deep Space 9 (DS9). Do note that Star Trek series normally need about a season to find their footing. Season 1 of TNG was mid-tier but it still is a source of plenty of memes.

I think TNG is likely the better starting point. The original series (TOS) is painfully old fashioned, which could ve a good thing or bad depending on your tastes.