Here's my ideal Sonic game: it takes elements from the olden games and blends them with 3D elements, like the fanmade Sonic Robo-Blast 2 and, to a lesser extent, Sonic Heroes. The initial player characters are Sonic, Tails, and Knuckles, but more can be unlocked by beating the game with other characters, including Shadow (for the fangirls and sexually-confused fanboys), Espio, Fang/Nack, Amy, etc.
Like with Sonic Heroes and Sonic Riders, each character has different strengths and specialties that can be classified under either Speed, Flight, or Power. While each stage has a path all characters can travel through, there are different paths that can only be accessed by certain characters, leading to shortcuts or secret items. For example, in a given factory stage, There are four different paths. One path can be taken by all characters. One path is set on a fast-moving conveyor belt, which only a speedy character like Sonic can get past. Another is blocked off by a laser fence that flight-capable characters like Tails can clear by flying over them. The last path is blocked off by a tightly-secured door that only powerful characters like Knuckles can break down.
The ability to play as Super Sonic during normal gameplay will be present, but it will be the last and most difficult unlockable to earn: to get it, you must beat the game with all the characters, find all the Chaos Emeralds, and clear the extra boss.
Speaking of Chaos Emeralds, they will be hidden in each stage like in the early Master System and Game Gear games and in Sonic R. Some Emeralds will be hidden in secret areas that can only be travelled down by certain characters, encouraging multiple playthroughs.
As to story...well, who the fuck plays Sonic and Mario games for story? Eggman's trying to take over the world, you gotta stop him. Simple.