TAS was also my first Trek experience. I was only 2 when it premiered, but for some reason it was one of the earliest memories I have of watching anything on TV. Since my parents were fans of TOS since September 8, 1966, TAS was on the TV from that premiere.
The first episode that I clearly remember was "Eye Of The Beholder" when it first aired, but everything from the series stuck with me all through my watching of TOS later on (some memories had been comingled, with me at one point trying to find the TOS episode where Kirk has "Kirk is a Jerk" on his tunic!)
When Nickelodeon started showing it, we didn't yet have cable TV, but when we went to an Uncle's house for a family gathering, we had the TV on. Someone put Nickelodeon on, at about the time when an episode of TAS was going to come on.
We left it on, and the first TAS episode I was able to see for the first time in 11 or so years? "Eye Of The Beholder"...