Awesome idea!
I haven't played any of the handhelds, so my ranks are very console heavy.
Story/Plot
#1: Ocarina Of Time
#2: Majora's Mask
#3: A Link To The Past
Main Characters
#1: Ocarina Of Time
#2: Majora's Mask
#3: Twilight Princess
Minor Characters
#1: Skyward Sword
#2: Wind Waker
#3: Majora's Mask
Writing
#1: Majora's Mask
#2: Ocarina Of Time
#3: A Link To The Past
Overworld
#1: Ocarina Of Time
#2: A Link To The Past
#3: Majora's Mask
Side Quests
#1: Majora's Mask
#2: Wind Waker
#3: Skyward Sword
Collecting
#1: Skyward Sword
#2: Wind Waker
#3: Majora's Mask
Gimmicks/Innovations
#1: Ocarina Of Time
#2: Skyward Sword
#3: Majora's Mask
Dungeons
#1: Ocarina Of Time
#2: A Link To The Past
#3: Majora's Mask
Controls
#1: Skyward Sword
#2: Twilight Princess
#3: Wind Waker
Combat
#1: Skyward Sword
#2: Majora's Mask
#3: Wind Waker
Exploration
#1: Ocarina Of Time
#2: Skyward Sword
#3: A Link To The Past
Puzzles
#1: A Link To The Past
#2: Ocarina Of Time
#3: Majora's Mask
Items
#1: Ocarina Of Time
#2: Skyward Sword
#3: Twilight Princess
Bosses
#1: Twilight Princess
#2: A Link To The Past
#3: Skyward Sword
Graphics
#1: Twilight Princess
#2: Wind Waker
#3: Majora's Mask
Art Style
#1: Twilight Princess
#2: Majora's Mask
#3: Skyward Sword
Music
#1: Ocarina Of Time
#2: Majora's Mask
#3: A Link To The Past
Tone
#1: Majora's Mask
#2: Ocarina Of Time
#3: Twilight Princess
Best Zelda Ever
#1: Ocarina Of Time
#2: Majora's Mask
#3: Skyward Sword