If you're looking for an ongoing storyline, give DS9 a try. The arc doesn't start to become apparent until season 2, though.
With the exception of seasons 3+4 of Enterprise, the other Trek series consist primarily of standalone stories. There are a few recurring bad guys and the like, but little in the way of an actual story arc.
If you're adventurous a bit, you may want to give some of the fan-created Trek shows a try:
Of those, Hidden Frontier has by far the most episodes produced. Their quality was a bit dodgy at first, but they've improved massively since then. The 23rd-century (TOS-style) shows tend to use physical sets, while the 24-century shows tend to use green screened virtual sets. What's particularly fun, at least to me, is that we're now seeing a tendency for various fan-series to do crossovers with each other.