Island of Happiness was my favorite Harvest Moon game for the DS, and I highly recommend it to start. Seduce the witch or you're not a true man.

Grand Bazaar was just released in North America on August 24th, so you could give that a try, though I haven't picked it up yet myself so I can't really recommend it. It is the newest, however, so I can only assume they've improved on the previous games.
I mean, look! Jumping!It's a shame you aren't looking to play on the Wii, Tree of Tranquility was amazing as well. Actually, if you prefer a little action in your farm simulation, you may want to pick up Rune Factory (any of them, for Wii or DS, also translated by Natsume). It's very much like Harvest Moon, but it has a bit of emphasis on going around and hunting monsters in caves and stuff, in addition to the farm life.