Yo that's Greek to me -- you mean you can catch more variety of Pokemon after you beat the campaign? Is omega and alpha original 151 remakes?
No, they're Ruby/Sapphire (Generation 3) remakes.
Heart Gold/Soul Silver was Generation 2 remakes of Gold, Silver, Crystal. Which includes Kanto (Generation 1) as a post-game.
Fire Red/Leaf Green was a generation 3 remake of Generation 1 (Kanto). That's what you're looking for.
Unless you want modern, where Kanto isn't featured (yet, I'm sure they'll do another round of remakes in a while).
The original 151 can not be caught in these modern games UNTIL you beat the Elite 4. I dunno if X&Y (Generation 6) changed that, but the other generations were the same outside of Generation 2 which had the 151 included with the other 151.