It's pretty ridic fun, but I don't know which episodes are the best for a newbie. Hmmm, Illya doesn't actually get upgraded to main cast until the second season, and I'm currently kind of stalled there, mostly because I'm not used to the pacing.

Oooh, but if you're a classic Trek fan, both Shatner and Nimoy guest-starred in The Strigas Affair. That one has a good amount of Illya as well. (Plus, it features Nimoy doing a very bad Eastern European accent.)