I haven't played all of them, so I can't comment on the best, but I'll give you my favorites.
1. Friends of Mineral Town/Back to Nature
To me, this is the crowning achievement of the series, offering absolutely everything the series is known for with utmost polish. On top of more addictive, in-depth farming mechanics, it has a great cast of characters and a nice town.
2. Harvest Moon 64
Still the best game if you want to focus on relationships and story. It was my first, so there's a bit of nostalgia here, but I think it has the best atmosphere, characters, and town of the entire series, and their stories are better fleshed-out than the Back to Nature versions.
3. Animal Parade
No one talks about this one, but it feels like the swan's song of the series to me. Relationships have been deepened in this game, but on top of that, it has addictive farming mechanics, a well-constructed main plot that doesn't close too much off but unlocks things slowly and keeps you engaged in the process, and a nice, liesurely pace. It feels like the biggest of the games in some way, maybe because the days are longer, and it also feels oddly realistic. It gets points for reminding me both of Back to Nature and of Harvest Moon 64.
It's not my favorite, but it may be the best in the series, or neck-and-neck with Back to Nature.