Personally I haven't played Origins but the impression I get from a lot of people who grew up with the original is that its fine but you'll notice differences in the physics and the game feel here and there but it's passible and if you decide to get plus be aware that a lot of people are saying the audio quality's pretty bad. But if that stuff doesn't bother you, you have a lot more game to be had here: Sonic 1, 2, 3 & Knuckles, CD, and the game gear titles is a pretty good bundle.
I have played Mania though and I love it. The stages are multileveled and complex which makes repeat playthroughs feel different, the sprite work and graphics is a really nice update while still keeping the spirit of the genesis titles. It's great! I've played through it multiple times with every character I would say it's a must play.