My first Star Trek experience was in the early 70s, but I hated it.
I remember my dad watching both TOS and the Planet of the Apes when I was a kid. I thought both shows were weird, boring and creepy. Especially after Star Wars came out, Trek's sfx looked cheap and there was very little action. Turn on Six Million Dollar Man!
In 1979, I went to see ST:TMP with my family and loved the sfx, but the movie was just as weird and boring as the TV show. When we walked out of the theater, I asked my dad, "What was that cloud thing they went into?" He paused and said, "I'm not really sure."
I was blown away by STII:TWOK! Loved it! A local TV station showed "Space Seed" as the prequel to TWOK. I thought it was just OK, but I continued to see each movie as they came out and really liked them. I still wasn't a big fan of the TV show, but my friend and I would watch Star Trek at midnight in college to make fun of the acting and sfx. I remember watching the premiere of TNG (Encounter At Farpoint) and thought it was as weird and boring as TOS.
As the series went on and as I got older, I really started to get into Star Trek. The stories were insightful with great characters, social commentary and philosophy. This was grown-up SF and I was now getting what it was really all about! I became a real fan in 1989. Since then, I've seen every episode of each series, read nearly 300 novels and been to quite a few conventions.