If I'm looking for Classic Sonic, I usually play Sonic 3. It's crazy how overlooked Sonic 3 is compared to the others.
I don't connect it to SnK either because I prefer the MJ style miniboss music in Sonic 3.
If I'm looking for 3D and want a full play-through then I do Sonic Colors, as it's in my opinion, the most cohesive modern Sonic game as a whole, but if I'm just looking for a stage here and there, then I do Generations or Forces (underrated IMO).