I've never played a Sonic game. Well that's not true, there was that one on the PS2 with a dark edgy Shadow counterpart. What's the best to get the feeling of the classics?
Just emulate the Genesis games and play them in order, from Sonic 1 onwards. There are better versions of these games to play, but they're kind of a pain to set up and also have a bunch of non-vanilla stuff that you have to go out of your way to turn off, which will muddle a first time experience. (I'm referring to Sonic 1 Forever, Sonic 2 Absolute, Sonic 3 AIR, and Sonic CD Restored - I recommend you try these after playing the original versions so you know what's new and what's not. CD Restored also forces you to beat the game twice before you can unlock the original soundtracks which is fucking bizarre.) Avoid the Sonic Origins versions of these games like the plague.
I do recommend you play Sonic 1 first because it will force you to come to terms with Sonic's base controls and how to utilize his movement in the levels. If you play Sonic 2 first, you might end up using the spin dash as a crutch and never actually understand how the movement works without it. The game's like an hour long so there's no real reason to skip it.
If you want to continue past the Genesis games onto the Adventure series, then either play the Dreamcast versions or mod the Steam versions (which are completely busted on a default install); there are tons of guides on Steam for the latter option. Avoid the Gamecube versions.
Edit: I did a little digging and found
this MEGA upload of Sonic 1 Forever, Sonic 2 Absolute, Sonic 3 AIR, and the Sonic CD Decomp all set up with no strings attached. These versions run in widescreen at a consistent 60 FPS and add a bunch of features. If you play this, though, then you have to disable modded features, like the spin dash in Sonic 1, and re-enable vanilla mechanics, like the roll jump control lock. That's why I think you should just play the Genesis versions for your first time, and leave these versions for replays.
