If you have Netflix and Amazon Prime you are able to watch literally all of Star Trek with no cost to you other than the subscriptions you have already. If you only have Hulu for whatever reason, you can watch all the shows but not the movies (who does that anyway?).
Also, keep in mind I'm only listing streaming options that are covered by monthly fees already. For example Star Trek III: The Search for Spock is available on Amazon streaming for $2.99, but I'm not going to list it because it costs extra.
Star Trek Seasons 1-3 (1966)
This is the most obvious place to start. I've seen a few episodes here and there over the years, but never really enough to understand any of it in a grand scale. From what I remember, it is quite campy, but it was the sixties, what was I expecting? I am going to try to start here, but I honestly don't expect it to hold my attention enough. Hopefully it will!
Star Trek: The Original Series on Netflix
Star Trek: The Original Series on Amazon Streaming
Star Trek: The Original Series on Hulu
Star Trek: The Original Series on Amazon Streaming
Star Trek: The Original Series on Hulu
Star Trek: The Animated Series (1973)
Apparently due to fan demand, the crew from the original show re-appeared in animated form in 1973. This seems to be a continuation of the original series. I have read that this was canon at some point, then it was decided it would be longer be canon. I'm going to try to watch it all, but I'm not really sure I'll be able to handle this. I find trouble trying to watch any animated made prior to the late '80s. It just doesn't hold my attention unforunately. I'll certainly try though!
Star Trek: The Animated Series on Netflix
Star Trek: The Motion Picture (1979)
This is where I was told to start watching Star Trek. Apparently the quality really begins to improve and it is much less cheesy. So, if I can't get through the first series, I'll just move to this. Please be aware there is apparently a director's cut, which is probably better, and I don't believe it is streaming anywhere.
Star Trek II: The Wrath of Khan (1982)
I have personally been informed that this is the best Star Trek anything ever. I'm definitely looking forward to watching it, Star Trek: Into Darkness spoilers here...After watching the new one featuring Khan, I'm very interested in the character. I'm also told Into Darkness and this have many similarities, I'm excited to find out what.
Star Trek III: The Search for Spock (1984)
Without reading the synopsis, I'm going to assume Wrath of Khan ends like Into Darkness did but Spock dies? Then they go somewhere to revive him? Apparently Leonard Nimoy, who plays Spock, directed this film and the next one.
