Friends of Mineral Town is my favorite. I didn't like HM64, I thought it was boring, simple, an eyesore, and you had no cooking system. Back to Nature was a massive improvement, and Friends of Mineral Town was a massive improvement over Back to Nature.
My mother loves A Wonderful Life but (spoiler alert) you only get ten years in the game. Save the Homeland was too focused on story, but Hero of Leaf Valley improves on Save the Homeland greatly, even letting you free-play like a normal Harvest Moon.
Never played the SNES one but I'm going to assume it's much simpler than the later games and it'll probably feel watered-down to me compared to later releases.
A Tale of Two Towns is also very good, it's for either the DS or 3DS and it does a lot of things right, it feels like we finally got an improvement over FoMT, it doesn't have the game-breaking BS that other recent games like Sunshine Isles had, and it takes some cues from the recent DS games and makes them work in a proper Harvest Moon. I highly recommend it, it's my second-favorite in the series.
The Rune Factory games for the DS are good, they add RPG elements and an interesting Monster Rancher feel, but the Wii game had one thing about it that ruined the entire game - those freaking spirits. You had to maintain them every week, it was a major pain and it distracted from other parts of the game too much.