After you get past the first few episodes (where they were finding their way with the show), TOS is very much like THE SIMPSONS. It doesn't have continuity so much as consistency. The characters don't really change and evolve. There is little if any reference to past episodes. That was the style of most TV at the time.
So watch the first handful of episodes in production order to watch the show evolve into it's "final" form. Then...seriously...watch the rest of the show in any order. It doesn't matter. Get yourself an episode guide and pick out one that seems interesting. Even the worst episodes of TOS usually have something watchable about them. "Spock's Brain" which is commonly regarded as one of, if not THE worst episode is very watchable if you approach it as a comedy. I don't watch it often, but have a lot of fun whenever I do.
The exception is "The Alternative Factor". That episode is bad on every level.
So watch the first handful of episodes in production order to watch the show evolve into it's "final" form. Then...seriously...watch the rest of the show in any order. It doesn't matter. Get yourself an episode guide and pick out one that seems interesting. Even the worst episodes of TOS usually have something watchable about them. "Spock's Brain" which is commonly regarded as one of, if not THE worst episode is very watchable if you approach it as a comedy. I don't watch it often, but have a lot of fun whenever I do.
The exception is "The Alternative Factor". That episode is bad on every level.