Watch Next Generation or a few episodes of OG Star Trek & then seeing Wrath of Khan movie.
Starting with Next Generation isn't a bad option I think. The beginning is rough at parts but has some really good episodes in it. The series got much better after season 2. You could follow a skip list to skip over the episode that are deemed horrible on your first watch to make it all easier. It's worth going back later to watch them though.
Deep space nine follows up an event that occured in Next Generation, so that show might be confusing till you watch NG.
Voyager is pretty much self-contained since that's a big part of the story lol. Only thing that could be confusing would be a character that's sorta important later on that is from NG. It isn't much but just something to state if stuff like that bothers you.
Enterprise is a pretty okay show I think. It's the earliest show in the timeline and mankind's first exploration. People don't like it for some reasons that are completely justified but it's never been anything to stop me from enjoying it. Might be best to watch this after others because it is different.
OG Star Trek is a fun series to watch. Really episodic so you can find some of the best episodes and try just watching those. Watch 3/4 of the best (including the one was Khan) and then watch the movie "Star Trek 2 Wrath of Khan".