Playable characters I would like:
1. Sonic (No boost, drift, or quickstep. Light speed dash on ANY trail of rings, Stomp [yes I prefer it over bounce bracelet] Homing attack, spin attack and slide.)
2. Shadow (move set from sonic 06 was cool, perhaps just an improvement on that)
3. Tails (mech from SA2)
4. Blaze (I'm not sure, might be interesting though)
5. Knuckles (perhaps a werehog fighting style but more fast-pased.)
I can't think of any others right now... Maybe Espio would be interesting? I'm not sure how I would like it story-wise. A bit more in-depth than the last few games would be nice.
Bring back Big the cat and his fishing levels.
It's what made Adventure 1 so "special".
How would Big The Cat work without fishing? Sonic Heroes utilized his fishing rod as a weapon, but I don't see that as a beneficial aspect to gameplay.
As for characters, I think there should be 6 playable max with the usual trio. The other characters I could see are Shadow and Rouge. The last character could be reserved for a new non-hedgehog character I suppose, or Blaze.
I do wonder though, should each character have their own path like Sonic Adventure 1? Or should it all be tied into one thing like Sonic Adventure 2?
Like a generic path, a lower path, Knuckles and Tails can do higher paths that cater specifically to flying, or gliding and climbing, and perhaps paths for Sonic that can only be opened with spindash. (I am a firm believer in not giving anyone but Sonic or Shadow spindash.)
Also, I think it would be cool to add extra non-story essential characters just for the sake of variety that have slightly different skills or help unlock a hardmode and/or easy mode. Extra unlockable characters and missions are always cool.
I'm going to be completely serious here: I believe Sonic Adventure 3 should be a revamped version of 06. Because 06 did TRY to be Adventure 3, it just failed miserably.
I want to see 06 with reworked physics, better moveset for each character (like, take Tails' moveset from SA1, Rouge's moveset from SA2 etc), better psychokinesis for Silver, drop Elise from the story, fix the stupid paradoxes of the time travel, etc etc.
Also, by now, I would be happy to see Modern Sonic style gameplay with Generations-like level design (Crisis City in Generations was PERFECT for that concept), Boost, and other characters having a similar moveset but with a rather weak Spindash instead of boost.
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Naw, I'm kidding. I dislike calling Sonic 06 Sonic Adventure 3, though. I don't see many people calling Super Mario Galaxy 2 by Super Mario 64 4. However, a revamp to actually complete the game would be nice. Along with a chance to change stuff. Throwing rings as an attack was just flat out annoying. As for time paradoxes, I don't think you're going to make a time travel story without having paradox's in some manner.