My favourite is DS9, best acting, storyline and characters. But it takes a bit of time to become really great and it's quite different from the rest, so you'd be better off starting with The Next Generation, which is the classic Trek stuff or with Voyager, it looks better and it's more entertaining. TNG is being remastered now and they'll start releasing episodes in better quality soon, so you might want to wait for that.
I think Enterprise is underrated, yeah, it had some flaws, but I still loved it, and I would love to see films with that cast about the Romulan War, instead of anything from JJ. You guessed right, I don't like what he and his gang did with Star Trek... (My dream is to see a DS9 film or two, or a mini-series, or a direct-to-DVD film, something, but I know that it won't happen...

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I haven't seen much from The Original Series, but it didn't age well, even if the stories are great, the acting and everything else makes it hard to watch, for me at least. I've seen all of their films though, and liked most of them.