In a presentation the professor asked me a question that, thinking about it today, I answered incorrectly, but I did it with such conviction, even after the professor questioned me again, that in the end he left me alone, gave me a good grade and even some classmates asked me advice.
Moral of the story: confidence is stronger than the truth. If you see someone very confident in what they say, it doesn't necessarily mean they are telling The Truth.
Sonic fan for more than two decades here! It's always great to see more people interested in the franchise!
I would say that maybe it would be good to start with Sonic Generations (or Sonic x Shadow Generations if you can afford it, which is the same but with the Shadow The Hedgehog story as an extra), so you get familiar with the gameplay of both classic and modern games, have a sense of where it's going and decide whether to go ahead or not.
I see that your interest is more focused on the characters and their dynamics, fantastic! the best part of the franchise in my opinion!. In that sense I would say that your best option to go deeper after Sonic Generations would be the mythical Adventure saga (Adventure 1 and Adventure 2). They are the games in which much more emphasis was put on the characters and the story.
Already after this and if you are hooked is that I recommend that you play the classics. You can play Sonic 1, Sonic CD, Sonic 2 and Sonic 3 & Knuckles in Sonic Origins (although you can also emulate the Mega Drive games), and then there is Sonic Mania. Why not start with the classics? Because they are very much of their time: pure gameplay, simple and not so deep story, but very fun to play!
You talk about games, but let me recommend you to read the IDW Comics in a complementary way. They are REALLY good! If I remember correctly, one of the artists on the comics, Evan Stanley, worked on The Murder of Sonic the Hedgehog, and the story of the game plays out very similar to how the Comics read. It's also where you'll find the most depth in the characters (and you'll encounter the best story arc EVER written for the franchise, EVER).
To sum up:
Sonic Generations (Or Sonic x Shadow Generations)
Sonic Adventure 1 and 2
Sonic Origins (Which are Sonic 1, CD, 2, 3 & Knuckles)
Someone is gonna do it. Someone's gonna feed AI with the Terminator Saga, Ex Machina movie, I have no mouth and I must Scream and Westworld, just for the laughs.
I have never gone to such extremes. I may confuse trivial details, but at the moment I have not reached the point of being forced to ask others about things that I either misremember or don't remember at all.
I was thinking about trying to stop doubting my memory. To trust more that what I remember happened, and if it didn't, to accept it and move on. I could also take measures, like telling myself "I'm doing this" to make the difference between what I really did and what I imagined.
That sounds like a dope game idea.