Could be any game really, the only "sequel" to Pokemon main games were Pokemon Gold/Silver in the Kanto part (Again, "sequel"), there's also Fire Red/Leaf Green which are remakes of the first two games (JP versions anyway) so that's the best place to start in a story standpoint, if you find it a little bit difficult, you can just play Pokemon X/Y then.
My recommendation would be this: Pokemon Leaf Green/Fire Red > Pokemon HG/SS > Pokemon ORAS or straight R/S > Pokemon Diamond/Pearl or the definitive version Platinum > Pokemon Black/White > Pokemon B/W 2 > Pokemon X/Y.
That's about it, you can also play the spinoff pokemon games, like Pokemon Colosseum or Pokemon Conquest, depending on what you would prefer to play, most spinoff Pokemon games are very good tho.
Oh I see. So do you have to complete both versions of each pair to properly complete it?
Yes, you can use emulators to get them easily, I think VBA allowed you to "connect" two emulators in order to do multiplayer things, and that includes the trading aspect of the Pokemon games, not so sure about the DS emulators though.
But yes, you have to complete the two versions, is kinda like FE Fates except that the changes between one game and the other one are mostly Pokemon related, with some small changes of plot instead of changing everything alongside.