My first Animal Crossing was the Gamecube version for me. I think I was still in elementary school back then, so for me the game was very magical, everything about the game was novel and you really never knew what to expect. I loved collecting bugs and fish, and I loved that Blathers would give you a lesson about the news ones you brought him. It was always just fun to get home from school and play AC a few hours every evening.
As for the newer games, I feel like villager dialogue has gotten less diverse and spontaneous as in the original; that or maybe I'm too old. I've played every AC game released and its become less about villagers and more about creating beautifully themed homes to impress your friends.
I still think there's enough charm in the games if you're new to the series. I think some of the magic has been lost because of the internet though. There's not a whole lot of mystery when you can look up anything on Youtube or the Wiki and get all the info you need. The game is far more interesting when you discover things for yourself.