Regarding Garak - yes, you'd need to know Deep Space Nine. I don't think you'd need to watch it, though, just do some research with episode summaries and MemoryAlpha. It's a very good show, but given how much of it there is, and how dark it gets, it's not something I can say you should make an attempt to watch the whole way through.

There's about five to ten episodes from the whole series I'd say you ought to make time for, including the Tribbles episode - so maybe four to nine episodes to meet the characters when they're at their best, shake their hands, and then read about them elsewhere.