I've played the entire Animal Crossing series, and I can definitely tell you that if you want to try it, feel free to jump right into the newest iteration, on 3DS. It's a bunch better than the previous one. (I can give you details on how if you want, but you can just take my word for it.)
The thing with Animal Crossing is that it runs in real time, which is sometimes good and sometimes not good. Every day, there's new stock at the shops, new fruit on the trees. Different times of the day and different months of the year, there are different fish and bugs to be caught. And in a way, that nature also means that there's a limit to how long you'll want to/be able to play each day, because you will run out of stuff to do other than random fishing for cash. It's relaxing fun.
The down side is that it can sometimes feel like a chore or an obligation. There's new stuff at the shop every day, so you may feel like you have to make money and get in there and buy that stuff every day. You may feel like you need to get every item in the catalog, so you'll feel like you can never take the game out of your 3DS. (In fact, I'd recommend this one for download rather than retail purchase.)
I tend to play the game the first way, my wife tends to play it the second way. She must have every new AC that comes out, though, so she clearly enjoys playing it her way, and I enjoy it my way.