I never saw the old series in theaters, only VHS. Begins was my first Bat-theater experience. It's still the most times ive been in a theater for a Batman movie.
My introduction was Batman 89 and Returns soon after. I must have been 3-4 years old in the early 90s watching those movies and freaking out. Getting all the toys. Then it was the Animated Series.
I liked Batman Forever (Carrey, Kilmer, the scenes about his childhood actually freaked me out as a 7 year old kid). But I didn't like Two-Face or much of the Robin stuff.
Batman & Robin. I thank the lord I never saw that in theaters. I was 9 when I rented it, and even at that age, I couldn't watch the whole movie in one sitting

. I was a little kid and I still knew it was terrible!
I was always disappointed in the 90s, early 2000's because I wanted the Animated Series/Mask Of The Phantasm style to be brought to life in live-action. And instead I kept getting the opposite.
At the time of Batman Begins, I wasn't aware of all the classic comic/graphic novels by Miller, O'Neill, Loeb, etc. But it just blew my mind and the tone was what I loved about Batman. After that, that's when I started digging into the source material. It took me 16 years by that point but it was worth it. Even though the one comic I remember reading as a kid was Knightfall. So yeah, I didn't grow up on comics, I grew up on animated/live-action Batman first.