Sonic the Hedgehog
When you're playing as Sonic, grab the Bounce Bracelet (which gives Sonic the bounce ability) in the Pyramid Cave. Once you have the Bounce Bracelet, go to the City Escape stage to get the Magic Gloves, which aid in picking up enemies. You'll find the Light Shoes in the Metal Harbor stage; these allow Sonic to light dash. Pick up the Ancient Light in Green Forest for the light attack. If you want the ability to destroy metal boxes, pick up the Flame Ring in the Crazy Gadget stage. Get the Mystic Melody in the Final Rush stage to acquire the ability to rescue the Lost Chao.
Tails
When you're playing as Tails, pick up the Bazooka in the Eternal Engine stage. This allows you to destroy metal boxes. Once you have the Bazooka, head over to Prison Lane for the Laser Blaster and to the Hidden Base to acquire the Mystic Melody, so you can rescue the Lost Chao. For the hover ability, get the Booster on Mission Street.
Knuckles
Knuckles needs the Hammer Gloves to destroy metal boxes. You can find them in the Death Chamber. For the digging ability, get the shovel claw on Pumpkin Hill. Once you have those two items, travel to Wild Canyon for the Mystic Melody to rescue the Lost Chao, and go to Meteor Herd for the sunglasses that allow you to see hidden items. Get the Air Necklace in the Aquatic Mine for infinite air while underwater.
Shadow
Shadow's Air Shoes let him light dash -- snag them in the White Jungle. After you obtain the shoes, you can get the Flame Ring on the Radical Highway. Use it to destroy metal boxes. Grab the Ancient Light found in Sky Rail so you can perform light attacks. You'll also need the Mystic Melody, found in the Final Chase stage, to rescue the Lost Chao.
Doctor Eggman
Doctor Eggman can hover with the Jet Engine that is found in the Lost Colony. The Large Cannon found in the Weapons Bed aids in destroying metal boxes. Attain more health with the Protective Armor, which is found in the Cosmic Wall. If you have the Jet Engine, you can get the Mystic Melody in the Sand Ocean.
Rogue
Rogue gets the digging ability with the Pink Nails that you can find in the Egg Quarters stage. Destroy metal boxes with the Iron Boots, which are found in Mad Space. Travel with the Metal Boots to Security Hall to get the Treasure Scope for the ability to see hidden items. If you have the Pink Nails, get the Mystic Melody in Dry Lagoon to save the Lost Chao.