I was still in high school, but paid very close attention to the news even back then. After reading and watching everything I could get a hold of at that time (The New York Times, NY Post, Huntley/Brinkley on NBC News, mainly) I distinctly remember feeling confused about Oswald being left or right.
I was in high school too. I still remember a kid named Tim Sutton telling me that Kennedy had been shot. It was an hour or more before we learned he was dead.
You are right. The media somehow persuaded nearly everyone that Southern Right Wing Gun Owners were responsible. I mean they really did do that. It was also the force behind them finally passing the 68 gun control bill which was a very harsh law.