I watched TOS as a boy lying on my parents bed. Don't know how I actually got started, just one of those things. I watched "Batman" too, but I never got attached -- Star Trek, on the other hand, fell on my head like a boulder.
ST:TNG started just after high school, and I remember being in my family's rec room, watching "Encounter at Farpoint" with my friends and my girlfriend (whom I met due to a "Vulcans never bluff" pin she was wearing on her fluffy pink sweater). Picard and Data are / were the most fascinating characters for me. I liked Riker and his bead, Geordie and his visor. Worf, it took me a long time to warm up to him (I thought he really hit his stride in DS9), and the doctor just never managed to hook me like, say, Bashier and "The Doctor" did. Weasly I could take or leave. I have been rewatching TNG over the last month from the begining, and find the earlier seasons are much better than I remember.
For me, DS9 in the best ST show. I liked all of them, but somehow, DS9 captivated me were TNG merely fascinated me, if you know what I mean.