Deep Space Nine is my favorite Trek, and in my opinion, the best. My wife never really watched it and didn't care too much for it, now it is her favorite Trek series as well. It's timeless and doesn't age. Very relevant, even today.
Avery Brooks as Captain Sisko, is easily my favorite Captain, as he isn't "always by the book" so to speak, and he doesn't take any shit from anyone. Also, the actors, being series regulars or guest actors, they all do such an amazing job. Harris Yulin, in Duet for an example, is amazing in an amazing episode.
Definitely start with Season 1, as that will set everything up and develope the characters.