My suggestion of the 16 items to show are:
1. Bow
2. Boomerang
3. Magical Rod (Zelda 1)
4. Lamp/Candle
5. Magic Hammer
6. Lens of Truth
7. Recorder/Ocarina
8. Hookshot
9. Bottle (can be filled with a potion or bee)
10. Deku Leaf
11. Bug Catching Net
12. Fire Rod
13. Gnat Hat
14. Book of Mudora
15. Ice Rod
16. Roc's Cape
How these work:
Bow will shoot a sword beam that is retextured to an arrow (and also play an arrow sound)
Boomerang will stun enemies (by setting their speed to 0) for about 5 seconds, will not work on bosses, also kills dry bones.
Magical Rod will kill certain enemies that are immune to the sword (booes and dry bones)
Lamp/Candle will burn stuff and/or enemies that don't have nofireball=1.
Magic Hammer can destroy a certain block (retextured to a hammer peg)
Lens of Truth will reveal secrets (like the special block that only reveals when in statue form)
Recorder/Ocarina can act as a key to unlocking something.
Hookshot can be used to cross gaps (range is to the other half of the screen), can only attach to certain blocks (most non-ground tiles)
Bottle is self-explanatory.
Deku Leaf, can be used to slow falling speed (can not attack while floating down)
Bug Catching Net can catch an enemy (particularly retextured to a bee)
Fire Rod is basically the fire flower.
Gnat Hat allows you to scale down to the height of half a block.
Book of Mudora can allow you to get an answer to a clue (particularly riddles)
Ice Rod is basically the ice flower
Roc's Cape allows for an extra jump (but shortened)
How the boots, flippers, and glove will work:
There are 2 separate boots, Pegasus boots and hover boots. Pegasus boots allow for you to run (but bonk against a wall). Hover boots allow for hovering (length is likely the same as Peach's floating ability)
Flippers can allow for you to swim in water (lacking them basically makes you fall as if the water wasn't there).
Handy Glove can allow you to break blocks with your sword.