Play these games in this order:
>Heart Gold and Soul Silver for DS (emulate if they're too expensive for you)
This game is really good. Like, really, really good. It's the only pokemon game that let's you see your pokemon follow behind you. It's a remake of pokemon Gold, Silver, and Crystal, which are the sequels of Pokémon Red/Blue.
>Pokemon Black 2 / White 2 (Again, emulate if you want. If you care about plot, read up on Pokemon Black 1 and White 1. Wouldn't recommend playing them very much, though)
Pretty good games. Have a high number of Pokémon and a lot of good story.
If you aren't feeling those games, try playing Pokémon Platinum instead (see below).
>Pokémon X/Y
Also fine. Worth playing for the new content alone.
>Omega Ruby/Alpha Sapphire.
Well done remakes of Pokémon Ruby and Sapphire. Interesting mechanics and a very lively region.
I skipped some games but you should definitely try them all. I'll post them in order from least recent to most recent. Note that all these games will have lower numbers of pokemon in them because they hadn't been created yet. I'll list them here.
>Pokémon Crystal
This is personally my favorite Pokémon game. However it has a lot less Pokémon in it. Also, it was remade into Heart Gold/Soul Silver, which I recommended above. Was made after Pokémon Gold/Silver, kinda like how Pokémon Yellow was made after Red/Blue, so there's no reason to play those.
>Pokémon Fire Red/Leaf Green
Remakes of Red and Blue. Not much more to say.
>Pokémon Emerald
The third in the trio of Ruby, Sapphire, and Emerald, much like Pokémon Crystal. Beautiful region, but was remade into Omega Ruby and Alpha Sapphire, which I already recommended.
>Pokémon Platinum
Amazing game, a beautiful region, and a lot of lore. Not on the direct recommendations because I wanted to keep it as short as possible, but really, this is a great game. The third in the Diamond/Pearl/Platinum trio, like Emerald and Crystal.
There you go.
