I don’t do iTunes - you actually get physical possession of the video files or do have do be doing some kind of Apple iThing to watch episodes?
You download digital video files in m4v format, watchable on a Mac, iPad or iPhone via Apple iTunes media players. However, they're tied to your purchase and watchable on up to 5 machines authorized by you.
I use TunesKit to make mp4 format copies, which are playable on any media player on any machine. Since I own the original, I can make a copy for myself (legal speak here). And it gets rid of the annoyance of having to go through iTunes to check on it for each playing. TunesKit removes all that garbage.
As I said, the HD remastered series is wonderful to watch, as they upgraded the quality to look more like modern sci-fi space quality. It's not perfect, after all the series was made in the 1960s. For instance, in HD you can see the actors bump into stone archways and see the "stone" moving, and see plywood bracing on some scenery!