Sonic has a plethora of different ways to approach but mixing those up is key because none of them are inherently considered better than others in most situations so you can utilize different techniques and still get large rewards equally. However, it is very important to consider the matchup at all times; I feel a Sonic player should have a VERY deep understanding of every single character in the game in order to optimise his punish game in situations where the other player makes mistakes. These mistakes, in turn, can only be recognised if you know openings in the other character/player's neutral game and act accordingly.
Some of the movement/approach options I like to utilise:
Dash Dance > JC Grab
This approach is one of Sonic's more fundamental options in the neutral and is also used heavily by other characters such as Falcon/Fox but to a lesser extent. This is something I believe every Sonic player should be doing in every matchup but it is exceedingly easy to do so against slower characters or ones with limited approach options. Eg. Lucario, Bowser, DK, Charizard. You can also use a Gatling Grab alternatively against characters that crouch cancel a lot. Eg. Roy, Yoshi.
Platform Drop > Fair/Bair
You can do the fair either from a downwards drop from a platform, a wavedash off or a simple run off. I find this is a very quick and deceptive option to utilise because of how safe it is if you space it correctly; the startup is quick and can catch dash dancing characters beneath you off guard, even if you hit with the weak hitbox. Use this against characters you really struggle in the neutral against when on flat ground. Eg. Link, Falco, G&W. Bair hits more infrequently and doesn't lead into followups in the majority of situations but it helps reset the neutral and gives you time to position yourself favourably, I use this in all matchups.
Moonwalk > Ftilt or Jab > Grab
A risky option to say the least but it is useful as long as it is only used in moderation. Sonic's moonwalk is very quick and almost teleports you across the stage especially when using F-tilt to gain that extra range. You can also jab then grab out of the moonwalk or F-Smash/D-Smash if you feel daring. I use this more frequently against campy characters or characters that SHFFL a lot in neutral. Eg. Snake, ROB, Fox, Mario.
These are just three of the approach options I use, perhaps I'll talk later about some other ones that I do. Hope this helps guys