Nothing at all can match the charm of the original, and it's the most 'charm' game I can think of. There's so many little things to appreciate about it. Since it's aimed at kids, you could even get どうぶつの森e+ on Dolphin and set it to full furigana if you want, but the second best version is just the NA Gamecube edition from 2002. Emulate it, but don't be surprised if you get choppy fps between 'acres', it's just a result of how Dolphin works with some hardware.
Do you mean DS or 3DS?
New Leaf has more to do, and as a person that hasn't entered the series yet it's the best place for you to start. It has the most amount of customization, but it does feel like a "wide as an ocean, deep as a puddle" kind of game sometimes, especially in the castrated dialogue compared to the excellent localization of Population: Growing!.
I never played City Folk but it's regarded (universally) as the worst one, although some of its features sound neat and should have made a return. Ignore Happy Home Designer completely unless you have nothing to play and really want to place furniture.